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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.04552">arXiv:2208.04552</a> <span> [<a href="https://arxiv.org/pdf/2208.04552">pdf</a>, <a href="https://arxiv.org/format/2208.04552">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Gravity in binary systems at the fifth and sixth post-Newtonian order </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.04552v1-abstract-short" style="display: inline;"> Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.04552v1-abstract-full').style.display = 'inline'; document.getElementById('2208.04552v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.04552v1-abstract-full" style="display: none;"> Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective One-Body Hamiltonian, extending the applicability of our results to the late inspiral and merger phases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.04552v1-abstract-full').style.display = 'none'; document.getElementById('2208.04552v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 1 figure. Contribution to the proceedings of Loops and Legs in Quantum Field Theory - LL2022</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.13822">arXiv:2110.13822</a> <span> [<a href="https://arxiv.org/pdf/2110.13822">pdf</a>, <a href="https://arxiv.org/format/2110.13822">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2022.115900">10.1016/j.nuclphysb.2022.115900 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.13822v2-abstract-short" style="display: inline;"> Within an effective field theory method to general relativity, we calculate the fifth-order post--Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in--in formalism, on which we give a detailed account. The f… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.13822v2-abstract-full').style.display = 'inline'; document.getElementById('2110.13822v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.13822v2-abstract-full" style="display: none;"> Within an effective field theory method to general relativity, we calculate the fifth-order post--Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in--in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, $q_{82}, q_{63}, q_{44}, \bar{d_5}$ and $a_6$, can all be determined from the local contributions to periastron advance $K^{\rm loc,h}(\hat{E},j)$, without further assumptions on the structure of the symmetric mass ratio, $谓$, of the expansion coefficients of the scattering angle $蠂_k$. The $O(谓^2)$ contributions to the 5 PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.13822v2-abstract-full').style.display = 'none'; document.getElementById('2110.13822v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages LATEX, several figures, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 21--151, DO--TH 21/27, SAGEX--21--30 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl Phys B983 (2022) 115900 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.08630">arXiv:2101.08630</a> <span> [<a href="https://arxiv.org/pdf/2101.08630">pdf</a>, <a href="https://arxiv.org/ps/2101.08630">ps</a>, <a href="https://arxiv.org/format/2101.08630">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2021.136260">10.1016/j.physletb.2021.136260 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The 6th Post-Newtonian Potential Terms at $O(G_N^4)$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2101.08630v1-abstract-short" style="display: inline;"> We calculate the potential contributions of the Hamiltonian in harmonic coordinates up 6PN for binary mass systems to $O(G_N^4)$ and perform comparisons to recent results in the literature \cite{Bern:2021dqo} and \cite{Bini:2020nsb}. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.08630v1-abstract-full" style="display: none;"> We calculate the potential contributions of the Hamiltonian in harmonic coordinates up 6PN for binary mass systems to $O(G_N^4)$ and perform comparisons to recent results in the literature \cite{Bern:2021dqo} and \cite{Bini:2020nsb}. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.08630v1-abstract-full').style.display = 'none'; document.getElementById('2101.08630v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--199, DO-TH 20/06, SAGEX-20-08 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2010.13672">arXiv:2010.13672</a> <span> [<a href="https://arxiv.org/pdf/2010.13672">pdf</a>, <a href="https://arxiv.org/ps/2010.13672">ps</a>, <a href="https://arxiv.org/format/2010.13672">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Solar and Stellar Astrophysics">astro-ph.SR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2021.115352">10.1016/j.nuclphysb.2021.115352 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2010.13672v1-abstract-short" style="display: inline;"> We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post--Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.13672v1-abstract-full').style.display = 'inline'; document.getElementById('2010.13672v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2010.13672v1-abstract-full" style="display: none;"> We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post--Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also consider the non--local tail contributions. Further steps towards the complete calculation are discussed and first comparisons are given to results in the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.13672v1-abstract-full').style.display = 'none'; document.getElementById('2010.13672v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages Latex, 2 style files</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--062, DO--TH 20/04, SAGEX--20--10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.07145">arXiv:2003.07145</a> <span> [<a href="https://arxiv.org/pdf/2003.07145">pdf</a>, <a href="https://arxiv.org/ps/2003.07145">ps</a>, <a href="https://arxiv.org/format/2003.07145">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Solar and Stellar Astrophysics">astro-ph.SR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2020.135496">10.1016/j.physletb.2020.135496 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Testing binary dynamics in gravity at the sixth post-Newtonian level </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.07145v1-abstract-short" style="display: inline;"> We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the $G_N^3$ terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.07145v1-abstract-full').style.display = 'inline'; document.getElementById('2003.07145v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.07145v1-abstract-full" style="display: none;"> We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the $G_N^3$ terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature \cite{Bern:2019nnu,Damour:2019lcq}. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in \cite{Bern:2019nnu} or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to \cite{Bern:2019nnu}, but not to \cite{Damour:2019lcq}. This implies that we also agree on all observables with \cite{Bern:2019nnu} to the sixth post--Newtonian order to $G_N^3$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.07145v1-abstract-full').style.display = 'none'; document.getElementById('2003.07145v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--044, DO--TH 20/02, SAGEX--20--06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.01692">arXiv:2003.01692</a> <span> [<a href="https://arxiv.org/pdf/2003.01692">pdf</a>, <a href="https://arxiv.org/format/2003.01692">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2020.115041">10.1016/j.nuclphysb.2020.115041 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.01692v1-abstract-short" style="display: inline;"> We calculate the motion of binary mass systems in gravity up to the fourth post--Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying dimensional regularization. We construct the canonical transformations to ADM coordinates and to effective one body theory (EOB) to compare with other approaches. We sho… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.01692v1-abstract-full').style.display = 'inline'; document.getElementById('2003.01692v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.01692v1-abstract-full" style="display: none;"> We calculate the motion of binary mass systems in gravity up to the fourth post--Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying dimensional regularization. We construct the canonical transformations to ADM coordinates and to effective one body theory (EOB) to compare with other approaches. We show that intermediate poles in the dimensional regularization parameter $\varepsilon$ vanish in the observables and the classical theory is not renormalized. The results are illustrated for a series of observables for which we agree with the literature. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.01692v1-abstract-full').style.display = 'none'; document.getElementById('2003.01692v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 2 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 20--025, DO--TH 20/01, SAGEX--20--03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.04411">arXiv:1911.04411</a> <span> [<a href="https://arxiv.org/pdf/1911.04411">pdf</a>, <a href="https://arxiv.org/ps/1911.04411">ps</a>, <a href="https://arxiv.org/format/1911.04411">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Solar and Stellar Astrophysics">astro-ph.SR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> From Momentum Expansions to Post-Minkowskian Hamiltonians by Computer Algebra Algorithms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bl%C3%BCmlein%2C+J">J. Bl眉mlein</a>, <a href="/search/gr-qc?searchtype=author&query=Maier%2C+A">A. Maier</a>, <a href="/search/gr-qc?searchtype=author&query=Marquard%2C+P">P. Marquard</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a>, <a href="/search/gr-qc?searchtype=author&query=Schneider%2C+C">C. Schneider</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.04411v1-abstract-short" style="display: inline;"> The post-Newtonian and post-Minkowskian solutions for the motion of binary mass systems in gravity can be derived in terms of momentum expansions within effective field theory approaches. In the post-Minkowskian approach the expansion is performed in the ratio $G_N/r$, retaining all velocity terms completely, while in the post-Newtonian approach only those velocity terms are accounted for which ar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.04411v1-abstract-full').style.display = 'inline'; document.getElementById('1911.04411v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.04411v1-abstract-full" style="display: none;"> The post-Newtonian and post-Minkowskian solutions for the motion of binary mass systems in gravity can be derived in terms of momentum expansions within effective field theory approaches. In the post-Minkowskian approach the expansion is performed in the ratio $G_N/r$, retaining all velocity terms completely, while in the post-Newtonian approach only those velocity terms are accounted for which are of the same order as the potential terms due to the virial theorem. We show that it is possible to obtain the complete post-Minkowskian expressions completely algorithmically, under most general purely mathematical conditions from a finite number of velocity terms and illustrate this up to the third post-Minkowskian order given in \cite{Bern:2019crd}. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.04411v1-abstract-full').style.display = 'none'; document.getElementById('1911.04411v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages Latex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> DESY 19--18,DO--TH 19/21, SAGEX-19-25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1805.07240">arXiv:1805.07240</a> <span> [<a href="https://arxiv.org/pdf/1805.07240">pdf</a>, <a href="https://arxiv.org/ps/1805.07240">ps</a>, <a href="https://arxiv.org/format/1805.07240">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s41114-024-00048-7">10.1007/s41114-024-00048-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1805.07240v5-abstract-short" style="display: inline;"> Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order re… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.07240v5-abstract-full').style.display = 'inline'; document.getElementById('1805.07240v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1805.07240v5-abstract-full" style="display: none;"> Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to $d$-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up for the first time. The conservative dynamics of binary systems finds explicit presentation and discussion through the fifth post-Newtonian order for spinless masses. For masses with spin Hamiltonians are known through (next-to)$^3$-leading-order spin-orbit and spin-spin couplings as well as through next-to-leading order cubic and quartic in spin interactions. Parts of those are given explicitly. Tidal-interaction Hamiltonians are considered through (next-to)$^2$-leading post-Newtonian order. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin-orbit and spin1-spin2 couplings. The most important historical issues get pointed out. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.07240v5-abstract-full').style.display = 'none'; document.getElementById('1805.07240v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 May, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Major revision of G.Sch盲fer & P.Jaranowski, Living Rev Relativ 21, 7 (2018). Generally updated and improved. New Sections 6.3.3-6.3.5 on results at 5PN to 6PN order. New Section 8 on tidal interactions. Added or updated 65 references. This version is identical to G.Sch盲fer & P.Jaranowski, Living Rev Relativ 27, 2 (2024)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Living Rev Relativ 27, 2 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.01283">arXiv:1601.01283</a> <span> [<a href="https://arxiv.org/pdf/1601.01283">pdf</a>, <a href="https://arxiv.org/ps/1601.01283">ps</a>, <a href="https://arxiv.org/format/1601.01283">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.084014">10.1103/PhysRevD.93.084014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1601.01283v2-abstract-short" style="display: inline;"> The fourth post-Newtonian (4PN) two-body dynamics has been recently tackled by several different approaches: effective field theory, Arnowitt-Deser-Misner Hamiltonian, action-angle-Delaunay averaging, effective-one-body, gravitational self-force, first law of dynamics, and Fokker action. We review the achievements of these approaches and discuss the complementarity of their results. Our main concl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.01283v2-abstract-full').style.display = 'inline'; document.getElementById('1601.01283v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.01283v2-abstract-full" style="display: none;"> The fourth post-Newtonian (4PN) two-body dynamics has been recently tackled by several different approaches: effective field theory, Arnowitt-Deser-Misner Hamiltonian, action-angle-Delaunay averaging, effective-one-body, gravitational self-force, first law of dynamics, and Fokker action. We review the achievements of these approaches and discuss the complementarity of their results. Our main conclusions are: (i) the results of the first complete derivation of the 4PN dynamics [T.Damour, P.Jaranowski, and G.Sch盲fer, Phys. Rev. D 89, 064058 (2014)] have been, piecewise, fully confirmed by several subsequent works; (ii) the results of the Delaunay-averaging technique [T.Damour, P.Jaranowski, and G.Sch盲fer, Phys. Rev. D 91, 084024 (2015)] have been confirmed by several independent works; and (iii) several claims in a recent Fokker-action computation [L.Bernard et al., arXiv:1512.02876v2 [gr-qc]] are incorrect, but can be corrected by the addition of a couple of ambiguity parameters linked to subtleties in the regularization of infrared and ultraviolet divergences. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.01283v2-abstract-full').style.display = 'none'; document.getElementById('1601.01283v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Additional discussion of Fokker-type actions in Appendix A; new references added; identical to published version; 20 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 084014 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1508.01016">arXiv:1508.01016</a> <span> [<a href="https://arxiv.org/pdf/1508.01016">pdf</a>, <a href="https://arxiv.org/ps/1508.01016">ps</a>, <a href="https://arxiv.org/format/1508.01016">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.92.124043">10.1103/PhysRevD.92.124043 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1508.01016v2-abstract-short" style="display: inline;"> The paper gives full details of the computation within the canonical formalism of Arnowitt, Deser, and Misner of the local-in-time part of the fourth post-Newtonian, i.e. of power eight in one over speed of light, conservative Hamiltonian of spinless compact binary systems. The Hamiltonian depends only on the bodies' positions and momenta. Dirac delta distributions are taken as source functions. T… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1508.01016v2-abstract-full').style.display = 'inline'; document.getElementById('1508.01016v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1508.01016v2-abstract-full" style="display: none;"> The paper gives full details of the computation within the canonical formalism of Arnowitt, Deser, and Misner of the local-in-time part of the fourth post-Newtonian, i.e. of power eight in one over speed of light, conservative Hamiltonian of spinless compact binary systems. The Hamiltonian depends only on the bodies' positions and momenta. Dirac delta distributions are taken as source functions. Their full control is furnished by dimensional continuation, by means of which the occurring ultraviolet (UV) divergences are uniquely regularized. The applied near-zone expansion of the time-symmetric Green function leads to infrared (IR) divergences. Their analytic regularization results in one single ambiguity parameter. Unique fixation of it was successfully performed in T.Damour, P.Jaranowski, and G.Sch盲fer, Phys. Rev. D 89, 064058 (2014) through far-zone matching. Technically as well as conceptually (backscatter binding energy), the level of the Lamb shift in quantum electrodynamics is reached. In a first run a computation of all terms is performed in three-dimensional space using analytic Riesz-Hadamard regularization techniques. Then divergences are treated locally (i.e., around particles' positions for UV and in the vicinity of spatial infinity for IR divergences) by means of combined dimensional and analytic regularization. Various evolved analytic expressions are presented for the first time. The breakdown of the Leibniz rule for distributional derivatives is addressed as well as the in general nondistributive law when regularizing value of products of functions evaluated at their singular point. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1508.01016v2-abstract-full').style.display = 'none'; document.getElementById('1508.01016v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 August, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Slightly changed title; minor amendments added; misprints removed; identical with published version; 50 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 92, 124043 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.04618">arXiv:1503.04618</a> <span> [<a href="https://arxiv.org/pdf/1503.04618">pdf</a>, <a href="https://arxiv.org/ps/1503.04618">ps</a>, <a href="https://arxiv.org/format/1503.04618">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0264-9381/32/14/145001">10.1088/0264-9381/32/14/145001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Canonical center and relative coordinates for compact binary systems through second post-Newtonian order </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Georg%2C+I">Ira Georg</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1503.04618v2-abstract-short" style="display: inline;"> Based on a recent paper by Rothe and Sch盲fer on compact binary systems, explicit expressions for canonical center and relative coordinates in terms of standard canonical coordinates are derived for spinless objects up to second post-Newtonian approximation of Einstein's theory of gravity. The inverse relations, i.e. the dependence of the standard canonical coordinates on the canonical center and r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.04618v2-abstract-full').style.display = 'inline'; document.getElementById('1503.04618v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.04618v2-abstract-full" style="display: none;"> Based on a recent paper by Rothe and Sch盲fer on compact binary systems, explicit expressions for canonical center and relative coordinates in terms of standard canonical coordinates are derived for spinless objects up to second post-Newtonian approximation of Einstein's theory of gravity. The inverse relations, i.e. the dependence of the standard canonical coordinates on the canonical center and relative coordinates, are also given up to the second post-Newtonian approximation. The famous Pythagorean-theorem-type Lorentz-invariant relation between the system's total energy or Hamiltonian squared, the rest energy or mass squared - solely depending on relative coordinates -, and the total linear momentum squared are explicitly shown through second post-Newtonian approximation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.04618v2-abstract-full').style.display = 'none'; document.getElementById('1503.04618v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 March, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Improvements in the text</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class. Quantum Grav. 32 (2015) 145001 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1502.07245">arXiv:1502.07245</a> <span> [<a href="https://arxiv.org/pdf/1502.07245">pdf</a>, <a href="https://arxiv.org/format/1502.07245">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.91.084024">10.1103/PhysRevD.91.084024 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fourth post-Newtonian effective one-body dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1502.07245v2-abstract-short" style="display: inline;"> The conservative dynamics of gravitationally interacting two-point-mass systems has been recently determined at the fourth post-Newtonian (4PN) approximation [T.Damour, P.Jaranowski, and G.Sch盲fer, Phys. Rev. D 89, 064058 (2014)], and found to be nonlocal in time. We show how to transcribe this dynamics within the effective one-body (EOB) formalism. To achieve this EOB transcription, we develop a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.07245v2-abstract-full').style.display = 'inline'; document.getElementById('1502.07245v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1502.07245v2-abstract-full" style="display: none;"> The conservative dynamics of gravitationally interacting two-point-mass systems has been recently determined at the fourth post-Newtonian (4PN) approximation [T.Damour, P.Jaranowski, and G.Sch盲fer, Phys. Rev. D 89, 064058 (2014)], and found to be nonlocal in time. We show how to transcribe this dynamics within the effective one-body (EOB) formalism. To achieve this EOB transcription, we develop a new strategy involving the (infinite-)order-reduction of a nonlocal dynamics to an ordinary action-angle Hamiltonian. Our final, equivalent EOB dynamics comprises two (local) radial potentials, $A(r)$ and $\bar{D}(r)$, and a nongeodesic mass-shell contribution $Q(r,p_r)$ given by an infinite series of even powers of the radial momentum $p_r$. Using an effective action technique, we complete our 4PN-level results by deriving two different, higher-order conservative contributions linked to tail-transported hereditary effects: the 5PN-level EOB logarithmic terms, as well as the 5.5PN-level, half-integral terms. We compare our improved analytical knowledge to previous, numerical gravitational-self-force computation of precession effects. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.07245v2-abstract-full').style.display = 'none'; document.getElementById('1502.07245v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Minor amendments added; misprints removed; identical with published version; 18 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 91, 084024 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1406.0358">arXiv:1406.0358</a> <span> [<a href="https://arxiv.org/pdf/1406.0358">pdf</a>, <a href="https://arxiv.org/format/1406.0358">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.89.104055">10.1103/PhysRevD.89.104055 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Eccentric Motion of Spinning Compact Binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1406.0358v1-abstract-short" style="display: inline;"> The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.0358v1-abstract-full').style.display = 'inline'; document.getElementById('1406.0358v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1406.0358v1-abstract-full" style="display: none;"> The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theory easily treatable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.0358v1-abstract-full').style.display = 'none'; document.getElementById('1406.0358v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 June, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 89, 104055 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1401.4548">arXiv:1401.4548</a> <span> [<a href="https://arxiv.org/pdf/1401.4548">pdf</a>, <a href="https://arxiv.org/ps/1401.4548">ps</a>, <a href="https://arxiv.org/format/1401.4548">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.89.064058">10.1103/PhysRevD.89.064058 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1401.4548v2-abstract-short" style="display: inline;"> We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Sch盲fer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1401.4548v2-abstract-full').style.display = 'inline'; document.getElementById('1401.4548v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1401.4548v2-abstract-full" style="display: none;"> We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Sch盲fer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L.Blanchet and T.Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincar茅-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) nonlocal-in-time interaction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1401.4548v2-abstract-full').style.display = 'none'; document.getElementById('1401.4548v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 March, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 January, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Minor amendments added; misprints removed; identical with published version. 18 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 89, 064058 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.6829">arXiv:1303.6829</a> <span> [<a href="https://arxiv.org/pdf/1303.6829">pdf</a>, <a href="https://arxiv.org/ps/1303.6829">ps</a>, <a href="https://arxiv.org/format/1303.6829">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.111.021101">10.1103/PhysRevLett.111.021101 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Shah%2C+A">Abhay Shah</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.6829v2-abstract-short" style="display: inline;"> The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.6829v2-abstract-full').style.display = 'inline'; document.getElementById('1303.6829v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.6829v2-abstract-full" style="display: none;"> The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.6829v2-abstract-full').style.display = 'none'; document.getElementById('1303.6829v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, accepted version in Physical Review Letters (PRL)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.3225">arXiv:1303.3225</a> <span> [<a href="https://arxiv.org/pdf/1303.3225">pdf</a>, <a href="https://arxiv.org/ps/1303.3225">ps</a>, <a href="https://arxiv.org/format/1303.3225">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.87.081503">10.1103/PhysRevD.87.081503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.3225v1-abstract-short" style="display: inline;"> The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients 51 a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.3225v1-abstract-full').style.display = 'inline'; document.getElementById('1303.3225v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.3225v1-abstract-full" style="display: none;"> The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [Jaranowski/Sch盲fer, Phys. Rev. D 86, 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As application, the last stable circular orbit is determined as function of the symmetric-mass-ratio parameter. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.3225v1-abstract-full').style.display = 'none'; document.getElementById('1303.3225v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.0666">arXiv:1303.0666</a> <span> [<a href="https://arxiv.org/pdf/1303.0666">pdf</a>, <a href="https://arxiv.org/ps/1303.0666">ps</a>, <a href="https://arxiv.org/format/1303.0666">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Recent progress in spin calculations in the post-Newtonian framework and applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hartung%2C+J">Johannes Hartung</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.0666v1-abstract-short" style="display: inline;"> Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an introductory level. We will also discuss some checks of our (complicated and long) results in the first part of the talk. In the second part we will show how to apply our… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.0666v1-abstract-full').style.display = 'inline'; document.getElementById('1303.0666v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.0666v1-abstract-full" style="display: none;"> Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an introductory level. We will also discuss some checks of our (complicated and long) results in the first part of the talk. In the second part we will show how to apply our results to the calculation of the last stable circular orbit of such a binary system of black holes or neutron stars. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.0666v1-abstract-full').style.display = 'none'; document.getElementById('1303.0666v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages, Proceedings of the 13th Marcel Grossmann Meeting</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.6723">arXiv:1302.6723</a> <span> [<a href="https://arxiv.org/pdf/1302.6723">pdf</a>, <a href="https://arxiv.org/ps/1302.6723">ps</a>, <a href="https://arxiv.org/format/1302.6723">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/andp.201200271">10.1002/andp.201200271 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hartung%2C+J">Johannes Hartung</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.6723v2-abstract-short" style="display: inline;"> The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.6723v2-abstract-full').style.display = 'inline'; document.getElementById('1302.6723v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.6723v2-abstract-full" style="display: none;"> The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincar茅 algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.6723v2-abstract-full').style.display = 'none'; document.getElementById('1302.6723v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">56 pages, minor corrections to match published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ann. Phys. (Berlin) 525:359 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.3665">arXiv:1301.3665</a> <span> [<a href="https://arxiv.org/pdf/1301.3665">pdf</a>, <a href="https://arxiv.org/format/1301.3665">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.87.064035">10.1103/PhysRevD.87.064035 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.3665v2-abstract-short" style="display: inline;"> This publication will deal with an explicit determination of the time evolution of the spin orientation axes and the evolution of the orbital phase in the case of circular orbits under next-to-leading order spin-orbit interactions. We modify the method of Schneider and Cui proposed in ["Theoreme 眉ber Bewegungsintegrale und ihre Anwendungen in Bahntheorien", Verlag der Bayerischen Akademie der Wiss… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.3665v2-abstract-full').style.display = 'inline'; document.getElementById('1301.3665v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.3665v2-abstract-full" style="display: none;"> This publication will deal with an explicit determination of the time evolution of the spin orientation axes and the evolution of the orbital phase in the case of circular orbits under next-to-leading order spin-orbit interactions. We modify the method of Schneider and Cui proposed in ["Theoreme 眉ber Bewegungsintegrale und ihre Anwendungen in Bahntheorien", Verlag der Bayerischen Akademie der Wissenschaften, volume 212, 2005.] to iteratively remove oscillatory terms in the equations of motion for different masses that were not present in the case of equal masses. Our smallness parameter is chosen to be the difference of the symmetric mass ratio to the value 1/4. Before the first Lie transformation, the set of conserved quantities consists of the total angular momentum, the amplitudes of the orbital angular momentum and of the spins, $L, S_1,$ and $S_2$. In contrary, the magnitude of the total spin $S=|S_1+S_2|$ is not conserved and we wish to shift its non-conservation to higher orders of the smallness parameter. We perform the iterations explicitly to first order, while performing higher orders would mean no structural difference or harder mathematical difficulties. To apply this method, we develop a canonical system of spin variables reduced by the conservation law of total angular momentum, which is imposed on the phase space as a constraint. The result is an asymptotic series in $蔚$ that may be truncated appropriately considering the physical properties of the regarded system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.3665v2-abstract-full').style.display = 'none'; document.getElementById('1301.3665v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 2 figures in v2: added references [60] and [62], symbols in figures corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D87:064035,2013 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1207.6961">arXiv:1207.6961</a> <span> [<a href="https://arxiv.org/pdf/1207.6961">pdf</a>, <a href="https://arxiv.org/format/1207.6961">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0264-9381/30/1/015007">10.1088/0264-9381/30/1/015007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Hartung%2C+J">Johannes Hartung</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1207.6961v2-abstract-short" style="display: inline;"> In this article the quasi-Keplerian parameterisation for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin-orbit, next-to-next-to-leading order spin(1)-spin(2), and next-to-leading order spin-squared dynamics in the conservative regime. In… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.6961v2-abstract-full').style.display = 'inline'; document.getElementById('1207.6961v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1207.6961v2-abstract-full" style="display: none;"> In this article the quasi-Keplerian parameterisation for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin-orbit, next-to-next-to-leading order spin(1)-spin(2), and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity type variable $x$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.6961v2-abstract-full').style.display = 'none'; document.getElementById('1207.6961v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 December, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 July, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages, 2 figures, v2: update to match published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class. Quantum Grav. 30 (2013) 015007 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1207.5448">arXiv:1207.5448</a> <span> [<a href="https://arxiv.org/pdf/1207.5448">pdf</a>, <a href="https://arxiv.org/ps/1207.5448">ps</a>, <a href="https://arxiv.org/format/1207.5448">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.86.061503">10.1103/PhysRevD.86.061503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1207.5448v1-abstract-short" style="display: inline;"> The article presents the conservative dynamics of gravitationally interacting two-point-mass systems up to the eight order in the inverse power of the velocity of light, i.e.\ 4th post-Newtonian (4PN) order, and up to quadratic order in Newton's gravitational constant. Additionally, all logarithmic terms at the 4PN order are given as well as terms describing the test-mass limit. With the aid of th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.5448v1-abstract-full').style.display = 'inline'; document.getElementById('1207.5448v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1207.5448v1-abstract-full" style="display: none;"> The article presents the conservative dynamics of gravitationally interacting two-point-mass systems up to the eight order in the inverse power of the velocity of light, i.e.\ 4th post-Newtonian (4PN) order, and up to quadratic order in Newton's gravitational constant. Additionally, all logarithmic terms at the 4PN order are given as well as terms describing the test-mass limit. With the aid of the Poincar茅 algebra additional terms are obtained. The dynamics is presented in form of an autonomous Hamiltonian derived within the formalism of Arnowitt, Deser and Misner. Out of the 57 different terms of the 4PN Hamiltonian in the center-of-mass frame, the coefficients of 45 of them are derived. Reduction of the obtained results to circular orbits is performed resulting in the 4PN-accurate formula for energy expressed in terms of angular frequency in which two coefficients are obtained for the first time. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.5448v1-abstract-full').style.display = 'none'; document.getElementById('1207.5448v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 July, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">ReVTeX 4-1, 4 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1205.4530">arXiv:1205.4530</a> <span> [<a href="https://arxiv.org/pdf/1205.4530">pdf</a>, <a href="https://arxiv.org/format/1205.4530">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-6596/484/1/012018">10.1088/1742-6596/484/1/012018 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1205.4530v1-abstract-short" style="display: inline;"> A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1205.4530v1-abstract-full" style="display: none;"> A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1205.4530v1-abstract-full').style.display = 'none'; document.getElementById('1205.4530v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 May, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Conference proceedings for the 7th International Conference on Gravitation and Cosmology (ICGC2011), 4 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1110.2094">arXiv:1110.2094</a> <span> [<a href="https://arxiv.org/pdf/1110.2094">pdf</a>, <a href="https://arxiv.org/ps/1110.2094">ps</a>, <a href="https://arxiv.org/format/1110.2094">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.aop.2012.02.006">10.1016/j.aop.2012.02.006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1110.2094v3-abstract-short" style="display: inline;"> The present paper addresses open questions regarding the handling of the spin supplementary condition within the effective field theory approach to the post-Newtonian approximation. In particular it is shown how the covariant spin supplementary condition can be eliminated at the level of the potential (which is subtle in various respects) and how the dynamics can be cast into a fully reduced Hamil… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.2094v3-abstract-full').style.display = 'inline'; document.getElementById('1110.2094v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1110.2094v3-abstract-full" style="display: none;"> The present paper addresses open questions regarding the handling of the spin supplementary condition within the effective field theory approach to the post-Newtonian approximation. In particular it is shown how the covariant spin supplementary condition can be eliminated at the level of the potential (which is subtle in various respects) and how the dynamics can be cast into a fully reduced Hamiltonian form. Two different methods are used and compared, one based on the well-known Dirac bracket and the other based on an action principle. It is discussed how the latter approach can be used to improve the Feynman rules by formulating them in terms of reduced canonical spin variables. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.2094v3-abstract-full').style.display = 'none'; document.getElementById('1110.2094v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 March, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages, document changed to match published version, in press; Ann. Phys. (N. Y.) (2012)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annals of Physics 327:1494-1537,2012 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1109.1182">arXiv:1109.1182</a> <span> [<a href="https://arxiv.org/pdf/1109.1182">pdf</a>, <a href="https://arxiv.org/format/1109.1182">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.84.124005">10.1103/PhysRevD.84.124005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Wang%2C+H">Han Wang</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Zeng%2C+J">Jing Zeng</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1109.1182v2-abstract-short" style="display: inline;"> In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable for this kind of calculation. The results are valid for arbitrary many objects. The energy loss is then computed and compared to well-known results for the energy… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.1182v2-abstract-full').style.display = 'inline'; document.getElementById('1109.1182v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1109.1182v2-abstract-full" style="display: none;"> In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable for this kind of calculation. The results are valid for arbitrary many objects. The energy loss is then computed and compared to well-known results for the energy flux as a check. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1109.1182v2-abstract-full').style.display = 'none'; document.getElementById('1109.1182v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 September, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, v2: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D84:124005,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1012.3894">arXiv:1012.3894</a> <span> [<a href="https://arxiv.org/pdf/1012.3894">pdf</a>, <a href="https://arxiv.org/ps/1012.3894">ps</a>, <a href="https://arxiv.org/format/1012.3894">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1002/andp.201100007">10.1002/andp.201100007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1012.3894v2-abstract-short" style="display: inline;"> The article provides full-analytic gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. The semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic, is avoided for the first time. The article is a completion of a prev… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.3894v2-abstract-full').style.display = 'inline'; document.getElementById('1012.3894v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1012.3894v2-abstract-full" style="display: none;"> The article provides full-analytic gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. The semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic, is avoided for the first time. The article is a completion of a previous one (Tessmer and Sch盲fer, Phys. Rev. D 82, 124064 (2010)) to second post-Newtonian (2PN) order in the harmonic GW amplitude and conservative orbital dynamics. A fully analytical inversion formula of the Kepler equation in harmonic coordinates is provided, as well as the analytic time Fourier expansion of trigonometric functions of the eccentric anomaly in terms of sines and cosines of the mean anomaly. Tail terms are not considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.3894v2-abstract-full').style.display = 'none'; document.getElementById('1012.3894v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 April, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">48 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ann. Phys. (Berlin) 523 (2011) 813-864 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1006.3714">arXiv:1006.3714</a> <span> [<a href="https://arxiv.org/pdf/1006.3714">pdf</a>, <a href="https://arxiv.org/ps/1006.3714">ps</a>, <a href="https://arxiv.org/format/1006.3714">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.82.124064">10.1103/PhysRevD.82.124064 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1006.3714v2-abstract-short" style="display: inline;"> The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial freque… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.3714v2-abstract-full').style.display = 'inline'; document.getElementById('1006.3714v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1006.3714v2-abstract-full" style="display: none;"> The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial frequency due to radiation reaction are used to provide stationary phase approximations to the frequency-domain wave forms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.3714v2-abstract-full').style.display = 'none'; document.getElementById('1006.3714v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 June, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, submitted to PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D82:124064,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1003.2735">arXiv:1003.2735</a> <span> [<a href="https://arxiv.org/pdf/1003.2735">pdf</a>, <a href="https://arxiv.org/ps/1003.2735">ps</a>, <a href="https://arxiv.org/format/1003.2735">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0264-9381/27/16/165005">10.1088/0264-9381/27/16/165005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Tessmer%2C+M">Manuel Tessmer</a>, <a href="/search/gr-qc?searchtype=author&query=Hartung%2C+J">Johannes Hartung</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1003.2735v4-abstract-short" style="display: inline;"> A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.2735v4-abstract-full').style.display = 'inline'; document.getElementById('1003.2735v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.2735v4-abstract-full" style="display: none;"> A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted of 0PN order. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.2735v4-abstract-full').style.display = 'none'; document.getElementById('1003.2735v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages, 1 figure, published in CQG. Current version: we removed a remark and clarified the derivation of the orbital element \e_phi</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class. Quantum Grav. 27 165005 (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1003.0561">arXiv:1003.0561</a> <span> [<a href="https://arxiv.org/pdf/1003.0561">pdf</a>, <a href="https://arxiv.org/ps/1003.0561">ps</a>, <a href="https://arxiv.org/format/1003.0561">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Ledvinka%2C+T">Tomas Ledvinka</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a>, <a href="/search/gr-qc?searchtype=author&query=Bicak%2C+J">Jiri Bicak</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1003.0561v1-abstract-short" style="display: inline;"> The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.0561v1-abstract-full').style.display = 'inline'; document.getElementById('1003.0561v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.0561v1-abstract-full" style="display: none;"> The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.0561v1-abstract-full').style.display = 'none'; document.getElementById('1003.0561v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages, to appear in the proceedings of the 12th Marcel Grossmann Meeting, Paris, July 2009</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1003.0390">arXiv:1003.0390</a> <span> [<a href="https://arxiv.org/pdf/1003.0390">pdf</a>, <a href="https://arxiv.org/ps/1003.0390">ps</a>, <a href="https://arxiv.org/format/1003.0390">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.3448924">10.1063/1.3448924 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Rothe%2C+T+J">Tilman J. Rothe</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1003.0390v1-abstract-short" style="display: inline;"> The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.0390v1-abstract-full').style.display = 'inline'; document.getElementById('1003.0390v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.0390v1-abstract-full" style="display: none;"> The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.0390v1-abstract-full').style.display = 'none'; document.getElementById('1003.0390v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Math. Phys. 51, 082501, 2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1002.4552">arXiv:1002.4552</a> <span> [<a href="https://arxiv.org/pdf/1002.4552">pdf</a>, <a href="https://arxiv.org/ps/1002.4552">ps</a>, <a href="https://arxiv.org/format/1002.4552">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.81.084014">10.1103/PhysRevD.81.084014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Fourth-post-Newtonian-exact approximation to General Relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Brizuela%2C+D">David Brizuela</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1002.4552v2-abstract-short" style="display: inline;"> An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers natur… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.4552v2-abstract-full').style.display = 'inline'; document.getElementById('1002.4552v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1002.4552v2-abstract-full" style="display: none;"> An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers naturally the conformal-flat-condition (CFC) approach by Isenberg, Wilson, and Mathews and the improved second PN-order exact approach CFC+. For stationary configurations, like Kerr black holes, agreement with General Relativity is achieved even through 5PN order. In addition, a particularly interesting 2PN-exact waveless approximation is analyzed in detail, which results from imposing more restrictive conditions. The proposed scheme can be considered as a further development on the waveless approach suggested by Schaefer and Gopakumar [Phys. Rev. D {\bf 69}, 021501 (2004)]. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.4552v2-abstract-full').style.display = 'none'; document.getElementById('1002.4552v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 April, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 February, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Replaced by the published version. Some clarifications and references added.</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D81:084014,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1002.3057">arXiv:1002.3057</a> <span> [<a href="https://arxiv.org/pdf/1002.3057">pdf</a>, <a href="https://arxiv.org/ps/1002.3057">ps</a>, <a href="https://arxiv.org/format/1002.3057">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> ADM canonical formulation with spin and application to post-Newtonian approximations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">J. Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">S. Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">G. Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1002.3057v1-abstract-short" style="display: inline;"> Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be used in future gravitational wave astronomy. We focus on the extension of the ADM canonical formalism to spinning binary black holes. Using the global Poincare… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.3057v1-abstract-full').style.display = 'inline'; document.getElementById('1002.3057v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1002.3057v1-abstract-full" style="display: none;"> Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be used in future gravitational wave astronomy. We focus on the extension of the ADM canonical formalism to spinning binary black holes. Using the global Poincare invariance of asymptotically flat spacetimes as the most important guiding consistency condition, this extension can be constructed order by order in the PN approximation. We were able to reach a high order both in the spin power and the PN counting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.3057v1-abstract-full').style.display = 'none'; document.getElementById('1002.3057v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 February, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, Proceedings of the 12th Marcel Grossman Meeting</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1002.2093">arXiv:1002.2093</a> <span> [<a href="https://arxiv.org/pdf/1002.2093">pdf</a>, <a href="https://arxiv.org/ps/1002.2093">ps</a>, <a href="https://arxiv.org/format/1002.2093">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0264-9381/27/13/135007">10.1088/0264-9381/27/13/135007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1002.2093v2-abstract-short" style="display: inline;"> Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrup… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.2093v2-abstract-full').style.display = 'inline'; document.getElementById('1002.2093v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1002.2093v2-abstract-full" style="display: none;"> Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.2093v2-abstract-full').style.display = 'none'; document.getElementById('1002.2093v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 June, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 February, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, minor changes to match published version at CQG</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Steven Hergt et al 2010 Class. Quantum Grav. 27 135007 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0910.2857">arXiv:0910.2857</a> <span> [<a href="https://arxiv.org/pdf/0910.2857">pdf</a>, <a href="https://arxiv.org/ps/0910.2857">ps</a>, <a href="https://arxiv.org/format/0910.2857">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Post-Newtonian methods: Analytic results on the binary problem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0910.2857v1-abstract-short" style="display: inline;"> A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0910.2857v1-abstract-full').style.display = 'inline'; document.getElementById('0910.2857v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0910.2857v1-abstract-full" style="display: none;"> A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field equations, the generalized isotropic ones of the canonical formalism of Arnowitt, Deser, and Misner and the harmonic ones of the Lorentz-covariant Fock-de Donder approach. Conserved quantities of isolated systems are identified and the Poincar茅 algebra is introduced. Post-Newtonian expansions are performed in the near and far (radiation) zones. The natural fitting of multipole expansions to post-Newtonian schemes is emphasized. The treated matter models are ideal fluids, pure point masses, and point masses with spin and mass-quadrupole moments modelling rotating black holes. Various Hamiltonians of spinning binaries are presented in explicit forms to higher post-Newtonian orders. The delicate use of black holes in post-Newtonian expansion calculations and of the Dirac delta function in general relativity find discussions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0910.2857v1-abstract-full').style.display = 'none'; document.getElementById('0910.2857v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 October, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">44 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the CNRS School in Orleans/France, eds. L. Blanchet, A. Spallicci, and B. Whiting</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0907.1967">arXiv:0907.1967</a> <span> [<a href="https://arxiv.org/pdf/0907.1967">pdf</a>, <a href="https://arxiv.org/ps/0907.1967">ps</a>, <a href="https://arxiv.org/format/0907.1967">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1209/0295-5075/87/50004">10.1209/0295-5075/87/50004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Canonical formulation of self-gravitating spinning-object systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0907.1967v3-abstract-short" style="display: inline;"> Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position, linear momentum and spin variables fulfill standard Poisson bracket relations. A spatially symmetric time gauge for the tetrad field is introduced. The achieved form… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.1967v3-abstract-full').style.display = 'inline'; document.getElementById('0907.1967v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0907.1967v3-abstract-full" style="display: none;"> Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position, linear momentum and spin variables fulfill standard Poisson bracket relations. A spatially symmetric time gauge for the tetrad field is introduced. The achieved formulation is of fully reduced form without unresolved constraints, supplementary, gauge, or coordinate conditions. The canonical field momentum is not related to the extrinsic curvature of spacelike hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of freedom to the Einstein form of the metric field is suggested. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.1967v3-abstract-full').style.display = 'none'; document.getElementById('0907.1967v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 April, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 July, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages. v2: extended version; identical to the published one. v3: corrected misprints in (24) and (39); improved notation; added note regarding a further reference.</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Europhys.Lett.87:50004,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.4772">arXiv:0903.4772</a> <span> [<a href="https://arxiv.org/pdf/0903.4772">pdf</a>, <a href="https://arxiv.org/ps/0903.4772">ps</a>, <a href="https://arxiv.org/format/0903.4772">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.80.088501">10.1103/PhysRevD.80.088501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0903.4772v2-abstract-short" style="display: inline;"> It is argued that the tetrad in a recent paper by Porto and Rothstein on gravitational spin-spin coupling should not have the given form. The fixation of that tetrad was suggested by Steinhoff, Hergt, and Schaefer as a possible source for the disagreement found in the spin-squared dynamics. However, this inconsistency will only show up in the next-to-leading order spin-orbit dynamics and not in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4772v2-abstract-full').style.display = 'inline'; document.getElementById('0903.4772v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.4772v2-abstract-full" style="display: none;"> It is argued that the tetrad in a recent paper by Porto and Rothstein on gravitational spin-spin coupling should not have the given form. The fixation of that tetrad was suggested by Steinhoff, Hergt, and Schaefer as a possible source for the disagreement found in the spin-squared dynamics. However, this inconsistency will only show up in the next-to-leading order spin-orbit dynamics and not in the spin-squared dynamics. Instead, the disagreement found at the next-to-leading order spin-squared level is due to a sign typo in the spin-squared paper by Porto and Rothstein. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4772v2-abstract-full').style.display = 'none'; document.getElementById('0903.4772v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 October, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 4 pages, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D80:088501,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0902.3688">arXiv:0902.3688</a> <span> [<a href="https://arxiv.org/pdf/0902.3688">pdf</a>, <a href="https://arxiv.org/ps/0902.3688">ps</a>, <a href="https://arxiv.org/format/0902.3688">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1751-8113/42/31/315204">10.1088/1751-8113/42/31/315204 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the model of a classical relativistic particle of constant and universal mass and spin </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Kassandrov%2C+V">V. Kassandrov</a>, <a href="/search/gr-qc?searchtype=author&query=Markova%2C+N">N. Markova</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">G. Schaefer</a>, <a href="/search/gr-qc?searchtype=author&query=Wipf%2C+A">A. Wipf</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0902.3688v2-abstract-short" style="display: inline;"> The deformation of the classical action for a free relativistic particle recently suggested by A. Staruszkiewicz gives rise to a spin structure which constrains the values of the invariant mass and the invariant spin to be the same for any solution of the equations of motion. We prove that both these Casimir invariants, the square of the four-momentum vector and the square of the Pauli-Luba艅ski… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0902.3688v2-abstract-full').style.display = 'inline'; document.getElementById('0902.3688v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0902.3688v2-abstract-full" style="display: none;"> The deformation of the classical action for a free relativistic particle recently suggested by A. Staruszkiewicz gives rise to a spin structure which constrains the values of the invariant mass and the invariant spin to be the same for any solution of the equations of motion. We prove that both these Casimir invariants, the square of the four-momentum vector and the square of the Pauli-Luba艅ski pseudo-vector, preserve the same fixed values even in the presence of an arbitrary external electromagnetic field. In the "free" case, in the centre of mass reference frame, the particle moves along a circle of fixed radius. In a homogeneous magnetic field, a number of rotational "states" is possible with frequencies slightly different from the cyclotron frequency, and "phase-like" transitions with spin flops occure at some critical value of the particle's three-momentum. In the last section, the article of Kuzenko, Lyakhovich and Segal (1994) in which, in fact, an equivalent model had been proposed and elaborated, is briefly reviewed and compared with Staruszkiewicz's approach and our results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0902.3688v2-abstract-full').style.display = 'none'; document.getElementById('0902.3688v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 July, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 February, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 4 figures; some comments, important references and afterword added. Accepted to J. Phys. A: Math. Theor</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Phys.A42:315204,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0809.2208">arXiv:0809.2208</a> <span> [<a href="https://arxiv.org/pdf/0809.2208">pdf</a>, <a href="https://arxiv.org/ps/0809.2208">ps</a>, <a href="https://arxiv.org/format/0809.2208">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.124004">10.1103/PhysRevD.78.124004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincar茅 invariance </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0809.2208v2-abstract-short" style="display: inline;"> The fulfillment of the space-asymptotic Poincar茅 algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally $1/c^4$ spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in $G$, the expressions for the $S^3p$- and the $S^2p^2$-Hamiltonians are… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2208v2-abstract-full').style.display = 'inline'; document.getElementById('0809.2208v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0809.2208v2-abstract-full" style="display: none;"> The fulfillment of the space-asymptotic Poincar茅 algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally $1/c^4$ spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in $G$, the expressions for the $S^3p$- and the $S^2p^2$-Hamiltonians are completed. It is also shown that there are no quartic nonlinear $S^4$-Hamiltonians to linear order in $G$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2208v2-abstract-full').style.display = 'none'; document.getElementById('0809.2208v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 14 pages; center-of-mass-vector corrected Eq. (2.25) and modified coefficients of the Hamiltonian Eq. (7.3) and corresponding source terms Eqs. (7.5) and (7.6) following hereof; version to appear in Phys Rev D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:124004,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0809.2200">arXiv:0809.2200</a> <span> [<a href="https://arxiv.org/pdf/0809.2200">pdf</a>, <a href="https://arxiv.org/ps/0809.2200">ps</a>, <a href="https://arxiv.org/format/0809.2200">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.101503">10.1103/PhysRevD.78.101503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spin-squared Hamiltonian of next-to-leading order gravitational interaction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0809.2200v3-abstract-short" style="display: inline;"> The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arno… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2200v3-abstract-full').style.display = 'inline'; document.getElementById('0809.2200v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0809.2200v3-abstract-full" style="display: none;"> The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2200v3-abstract-full').style.display = 'none'; document.getElementById('0809.2200v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 November, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 10 pages, v2: minor improvements in the presentation, v3: added omission in Eq. (4) and corrected coefficients in the result, Eq. (9); version to appear in Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:101503,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0807.0214">arXiv:0807.0214</a> <span> [<a href="https://arxiv.org/pdf/0807.0214">pdf</a>, <a href="https://arxiv.org/ps/0807.0214">ps</a>, <a href="https://arxiv.org/format/0807.0214">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.100.251101">10.1103/PhysRevLett.100.251101 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Ledvinka%2C+T">Tomas Ledvinka</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a>, <a href="/search/gr-qc?searchtype=author&query=Bicak%2C+J">Jiri Bicak</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0807.0214v1-abstract-short" style="display: inline;"> The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.0214v1-abstract-full').style.display = 'inline'; document.getElementById('0807.0214v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0807.0214v1-abstract-full" style="display: none;"> The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0807.0214v1-abstract-full').style.display = 'none'; document.getElementById('0807.0214v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 July, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.Lett.100:251101,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0805.3136">arXiv:0805.3136</a> <span> [<a href="https://arxiv.org/pdf/0805.3136">pdf</a>, <a href="https://arxiv.org/ps/0805.3136">ps</a>, <a href="https://arxiv.org/format/0805.3136">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.77.104018">10.1103/PhysRevD.77.104018 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> ADM canonical formalism for gravitating spinning objects </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a>, <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0805.3136v2-abstract-short" style="display: inline;"> In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approxi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0805.3136v2-abstract-full').style.display = 'inline'; document.getElementById('0805.3136v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0805.3136v2-abstract-full" style="display: none;"> In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Schaefer [2], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [3], is presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0805.3136v2-abstract-full').style.display = 'none'; document.getElementById('0805.3136v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 October, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 May, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 18 pages. v1: published version. v2: corrected misprints in (8.4) and (9.3), updated references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D77:104018,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0804.2386">arXiv:0804.2386</a> <span> [<a href="https://arxiv.org/pdf/0804.2386">pdf</a>, <a href="https://arxiv.org/ps/0804.2386">ps</a>, <a href="https://arxiv.org/format/0804.2386">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/9789812834300_0441">10.1142/9789812834300_0441 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dimensional regularization of the gravitational interaction of point masses in the ADM formalism </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0804.2386v1-abstract-short" style="display: inline;"> The ADM formalism for two-point-mass systems in $d$ space dimensions is sketched. It is pointed out that the regularization ambiguities of the 3rd post-Newtonian ADM Hamiltonian considered directly in $d=3$ space dimensions can be cured by dimensional continuation (to complex $d$'s), which leads to a finite and unique Hamiltonian as $d\to3$. Some so far unpublished details of the dimensional-con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0804.2386v1-abstract-full').style.display = 'inline'; document.getElementById('0804.2386v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0804.2386v1-abstract-full" style="display: none;"> The ADM formalism for two-point-mass systems in $d$ space dimensions is sketched. It is pointed out that the regularization ambiguities of the 3rd post-Newtonian ADM Hamiltonian considered directly in $d=3$ space dimensions can be cured by dimensional continuation (to complex $d$'s), which leads to a finite and unique Hamiltonian as $d\to3$. Some so far unpublished details of the dimensional-continuation computation of the 3rd post-Newtonian two-point-mass ADM Hamiltonian are presented. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0804.2386v1-abstract-full').style.display = 'none'; document.getElementById('0804.2386v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 April, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To appear in "Proceedings of the 11th Marcel Grossmann Meeting on General Relativity", edited by H.Kleinert, R.T.Jantzen and R.Ruffini, World Scientific, Singapore, 2008</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0803.2348">arXiv:0803.2348</a> <span> [<a href="https://arxiv.org/pdf/0803.2348">pdf</a>, <a href="https://arxiv.org/ps/0803.2348">ps</a>, <a href="https://arxiv.org/format/0803.2348">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.77.104023">10.1103/PhysRevD.77.104023 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Gopakumar%2C+A">Achamveedu Gopakumar</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0803.2348v1-abstract-short" style="display: inline;"> Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Sch盲fer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.2348v1-abstract-full').style.display = 'inline'; document.getElementById('0803.2348v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0803.2348v1-abstract-full" style="display: none;"> Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Sch盲fer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a transparent Hamiltonian way and in Burke-Thorne gauge structure, the effects of gravitational radiation reaction into the above Skeleton dynamics with the help of 3.5PN accurate angular momentum flux for compact binaries in quasi-circular orbits to obtain a Semi-Analytic Puncture Evolution to model merging black-hole binaries. With the help of the TaylorT4 approximant at 3.5PN order, we perform a {\it first-order} comparison between gravitational wave phase evolutions in Numerical Relativity and our approach for equal-mass binary black holes. This comparison reveals that a modified Skeletonian reactive dynamics that employs flexible parameters will be required to prevent the dephasing between our scheme and Numerical Relativity, similar to what is pursued in the Effective One Body approach. A rough estimate for the gravitational waveform associated with the binary black-hole coalescence in our approach is also provided. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.2348v1-abstract-full').style.display = 'none'; document.getElementById('0803.2348v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 March, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D77:104023,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0803.0915">arXiv:0803.0915</a> <span> [<a href="https://arxiv.org/pdf/0803.0915">pdf</a>, <a href="https://arxiv.org/ps/0803.0915">ps</a>, <a href="https://arxiv.org/format/0803.0915">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.024009">10.1103/PhysRevD.78.024009 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0803.0915v1-abstract-short" style="display: inline;"> Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the Effective One Body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ``effective'' Hamiltonian and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.0915v1-abstract-full').style.display = 'inline'; document.getElementById('0803.0915v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0803.0915v1-abstract-full" style="display: none;"> Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the Effective One Body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ``effective'' Hamiltonian and the ``real'' one, (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta, (iii) a Kerr-type effective metric (with Pad茅-resummed coefficients) which depends on the choice of some basic ``effective spin vector'' $\bf{S}_{\rm eff}$, and which is deformed by comparable-mass effects, and (iv) an additional effective spin-orbit interaction term involving another spin vector $\bsigma$. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter $\hat{a}_{\rm LSO}\equiv c J_{\rm LSO}/\boldsymbol(G(H_{\rm LSO}/c^2)^2\boldsymbol)$. We find that the inclusion of NLO spin-orbit terms has a significant ``moderating'' effect on the dynamical characteristics of the circular orbits for large and parallel spins. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.0915v1-abstract-full').style.display = 'none'; document.getElementById('0803.0915v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 March, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX, 22 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:024009,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0712.1716">arXiv:0712.1716</a> <span> [<a href="https://arxiv.org/pdf/0712.1716">pdf</a>, <a href="https://arxiv.org/ps/0712.1716">ps</a>, <a href="https://arxiv.org/format/0712.1716">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Astrophysical Phenomena">astro-ph.HE</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.77.081501">10.1103/PhysRevD.77.081501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Steinhoff%2C+J">Jan Steinhoff</a>, <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0712.1716v2-abstract-short" style="display: inline;"> Based on recent developments by the authors a next-to-leading order spin(1)-spin(2) Hamiltonian is derived for the first time. The result is obtained within the canonical formalism of Arnowitt, Deser, and Misner (ADM) utilizing their generalized isotropic coordinates. A comparison with other methods is given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0712.1716v2-abstract-full" style="display: none;"> Based on recent developments by the authors a next-to-leading order spin(1)-spin(2) Hamiltonian is derived for the first time. The result is obtained within the canonical formalism of Arnowitt, Deser, and Misner (ADM) utilizing their generalized isotropic coordinates. A comparison with other methods is given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0712.1716v2-abstract-full').style.display = 'none'; document.getElementById('0712.1716v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 May, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 December, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 5 pages, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D77:081501,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0712.1515">arXiv:0712.1515</a> <span> [<a href="https://arxiv.org/pdf/0712.1515">pdf</a>, <a href="https://arxiv.org/ps/0712.1515">ps</a>, <a href="https://arxiv.org/format/0712.1515">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.77.104001">10.1103/PhysRevD.77.104001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hergt%2C+S">Steven Hergt</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0712.1515v4-abstract-short" style="display: inline;"> The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, respectively in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-orde… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0712.1515v4-abstract-full').style.display = 'inline'; document.getElementById('0712.1515v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0712.1515v4-abstract-full" style="display: none;"> The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, respectively in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black-hole binaries are derived. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0712.1515v4-abstract-full').style.display = 'none'; document.getElementById('0712.1515v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 December, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">REVTeX4, 20 pages, typos corrected in Eq. (124) and (130)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D77:104001,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0711.1048">arXiv:0711.1048</a> <span> [<a href="https://arxiv.org/pdf/0711.1048">pdf</a>, <a href="https://arxiv.org/ps/0711.1048">ps</a>, <a href="https://arxiv.org/format/0711.1048">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.77.064032">10.1103/PhysRevD.77.064032 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Damour%2C+T">Thibault Damour</a>, <a href="/search/gr-qc?searchtype=author&query=Jaranowski%2C+P">Piotr Jaranowski</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0711.1048v2-abstract-short" style="display: inline;"> A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins), which starts from the second-post-Newtonian metric (in ADM coordinates) generated by two spinless bodies, and computes the next-to-leading order precession, in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0711.1048v2-abstract-full').style.display = 'inline'; document.getElementById('0711.1048v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0711.1048v2-abstract-full" style="display: none;"> A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins), which starts from the second-post-Newtonian metric (in ADM coordinates) generated by two spinless bodies, and computes the next-to-leading order precession, in this metric, of suitably redefined ``constant-magnitude'' 3-dimensional spin vectors ${\bf S}_1$, ${\bf S}_2$. We prove the Poincar茅 invariance of our Hamiltonian by explicitly constructing ten phase-space generators realizing the Poincar茅 algebra. A remarkable feature of our approach is that it allows one to derive the {\it orbital} equations of motion of spinning binaries to next-to-leading order in spin-orbit coupling without having to solve Einstein's field equations with a spin-dependent stress tensor. We show that our Hamiltonian (orbital and spin) dynamics is equivalent to the dynamics recently obtained by Faye, Blanchet, and Buonanno, by solving Einstein's equations in harmonic coordinates. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0711.1048v2-abstract-full').style.display = 'none'; document.getElementById('0711.1048v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 April, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 November, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Few minor corrections made, 2 references added, some misprints removed</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D77:064032,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0703034">arXiv:gr-qc/0703034</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0703034">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0703034">ps</a>, <a href="https://arxiv.org/format/gr-qc/0703034">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/9789812834300_0042">10.1142/9789812834300_0042 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Post-Newtonian Approximations, Compact Binaries, and Strong-Field Tests of Gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Blanchet%2C+L">Luc Blanchet</a>, <a href="/search/gr-qc?searchtype=author&query=Grishchuk%2C+L+P">L P Grishchuk</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">Gerhard Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0703034v2-abstract-short" style="display: inline;"> This is an extended summary of the two parallel sessions held at MG11: PPN1 ``Strong Gravity and Binaries'' (chaired by L.B. and L.G.) and PPN2 ``Post-Newtonian Dynamics in Binary Objects'' (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0703034v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0703034v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0703034v2-abstract-full" style="display: none;"> This is an extended summary of the two parallel sessions held at MG11: PPN1 ``Strong Gravity and Binaries'' (chaired by L.B. and L.G.) and PPN2 ``Post-Newtonian Dynamics in Binary Objects'' (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places the delivered talks in a broader perspective of current studies in this area. One can find more details in individual contributions of the respective authors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0703034v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0703034v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, summary of PPN1 and PPN2 parallel sessions at MG11 (Berlin, August,2006); v.2: improvements in text, additional references, submitted to Proceedings</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0604060">arXiv:gr-qc/0604060</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0604060">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0604060">ps</a>, <a href="https://arxiv.org/format/gr-qc/0604060">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physleta.2007.03.036">10.1016/j.physleta.2007.03.036 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gravimagnetic effect of the barycentric motion of the Sun and determination of the post-Newtonian parameter gamma in the Cassini experiment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Kopeikin%2C+S+M">S. M. Kopeikin</a>, <a href="/search/gr-qc?searchtype=author&query=Polnarev%2C+A+G">A. G. Polnarev</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">G. Schaefer</a>, <a href="/search/gr-qc?searchtype=author&query=Vlasov%2C+I+Y">I. Yu. Vlasov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0604060v6-abstract-short" style="display: inline;"> The most precise test of the post-Newtonian gamma parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0604060v6-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0604060v6-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0604060v6-abstract-full" style="display: none;"> The most precise test of the post-Newtonian gamma parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field of the Sun, generated by its barycentric orbital motion, on the Shapiro delay. This non-stationary gravitational field of the Sun is associated with the Lorentz transformation of the metric tensor and the affine connection from the heliocentric to the barycentric frame of the solar system and can be treated as gravimagnetic field. The gravimagnetic field perturbs the propagation of a radio wave and contributes to its frequency shift at the level up to 4 10^{-13} that may affect the precise measurement of the parameter gamma in the Cassini experiment to about one part in 10,000. Our analysis suggests that the translational gravimagnetic field of the Sun can be extracted from the Cassini data, and its effect is separable from the space curvature characterized by the parameter gamma. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0604060v6-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0604060v6-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 April, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 1 figure, accepted to Physical Letters A</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.A367:276-280,2007 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/astro-ph/0412611">arXiv:astro-ph/0412611</a> <span> [<a href="https://arxiv.org/pdf/astro-ph/0412611">pdf</a>, <a href="https://arxiv.org/ps/astro-ph/0412611">ps</a>, <a href="https://arxiv.org/format/astro-ph/0412611">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Astrophysics">astro-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1051/0004-6361:20042602">10.1051/0004-6361:20042602 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Cerda-Duran%2C+P">P. Cerda-Duran</a>, <a href="/search/gr-qc?searchtype=author&query=Faye%2C+G">G. Faye</a>, <a href="/search/gr-qc?searchtype=author&query=Dimmelmeier%2C+H">H. Dimmelmeier</a>, <a href="/search/gr-qc?searchtype=author&query=Font%2C+J+A">J. A. Font</a>, <a href="/search/gr-qc?searchtype=author&query=Ibanez%2C+J+M">J. M. Ibanez</a>, <a href="/search/gr-qc?searchtype=author&query=Mueller%2C+E">E. Mueller</a>, <a href="/search/gr-qc?searchtype=author&query=Schaefer%2C+G">G. Schaefer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="astro-ph/0412611v1-abstract-short" style="display: inline;"> Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al (2002a,b), one of the most interesting such approximation is the so-called conformal flatness condition (C… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0412611v1-abstract-full').style.display = 'inline'; document.getElementById('astro-ph/0412611v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="astro-ph/0412611v1-abstract-full" style="display: none;"> Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al (2002a,b), one of the most interesting such approximation is the so-called conformal flatness condition (CFC) of Isenberg, Wilson and Mathews. Building on this previous work we present here new results from numerical simulations of relativistic rotational core collapse in axisymmetry, aiming at improving the dynamics and the gravitational waveforms. The computer code used for these simulations evolves the coupled system of metric and fluid equations using the 3+1 formalism, specialized to a new framework for the gravitational field equations which we call CFC+. In this approach we add new degrees of freedom to the original CFC equations, which extend them by terms of second post-Newtonian order. The corrections for CFC+ are computed solving a system of elliptic linear equations. The new formalism is assessed with time evolutions of both rotating neutron stars in equilibrium and gravitational core collapse of rotating polytropes. Gravitational wave signals for a comprehensive sample of collapse models are extracted using either the quadrupole formula or directly from the metric. We discuss our results on the dynamics and the gravitational wave emission through a detailed comparison between CFC and CFC+ simulations. The main conclusion is that, for the neutron star spacetimes analyzed in the present work, no significant differences are found among CFC, CFC+, and full general relativity, which highlights the suitability of the former. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('astro-ph/0412611v1-abstract-full').style.display = 'none'; document.getElementById('astro-ph/0412611v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 December, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages, 8 figures, submitted to A&A</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0411057">arXiv:gr-qc/0411057</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0411057">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0411057">ps</a>, <a href="https://arxiv.org/format/gr-qc/0411057">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.71.044021">10.1103/PhysRevD.71.044021 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Memmesheimer%2C+R">Raoul-Martin Memmesheimer</a>, <a href="/search/gr-qc?searchtype=author&query=Sch%C3%A4fer%2C+G">Gerhard Sch盲fer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="gr-qc/0411057v1-abstract-short" style="display: inline;"> The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian (3pN) order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincar茅 algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincar茅 group resp. the integrals of motion is achieved by imposing their a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0411057v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0411057v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0411057v1-abstract-full" style="display: none;"> The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian (3pN) order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincar茅 algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincar茅 group resp. the integrals of motion is achieved by imposing their action on the point mass coordinates to be identical with that of the usual infinitesimal Poincar茅 transformations. The second post-Coulombian approximation to the dynamics of two point charges as predicted by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0411057v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0411057v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 November, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages, submitted to Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D71:044021,2005 </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Schafer%2C+G&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div 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