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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <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/2407.20032">arXiv:2407.20032</a> <span> [<a href="https://arxiv.org/pdf/2407.20032">pdf</a>, <a href="https://arxiv.org/format/2407.20032">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"> The interaction between gravitational waves and a viscous fluid shell on a Schwarzschild background </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="2407.20032v1-abstract-short" style="display: inline;"> Previous work has shown that the interaction between gravitational waves (GWs) and a shell of viscous matter leads to damping of the GWs and heating of the matter, and that these effects may be astrophysically significant. This result was derived using the theory of linear perturbations about a Minkowki background, and in this work the model is extended to be more physically realistic by allowing… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.20032v1-abstract-full').style.display = 'inline'; document.getElementById('2407.20032v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.20032v1-abstract-full" style="display: none;"> Previous work has shown that the interaction between gravitational waves (GWs) and a shell of viscous matter leads to damping of the GWs and heating of the matter, and that these effects may be astrophysically significant. This result was derived using the theory of linear perturbations about a Minkowki background, and in this work the model is extended to be more physically realistic by allowing the background geometry to be Schwarzschild. It is found that the difference between using a Schwarzschild or Minkowski background is minimal when either $r\gg M$ or $位< M$, where $r$ is the radius of the shell, $位$ is the GW wavelength and $M$ is the mass of the system in geometric units (so that $1M_\odot=1.48$km). However, when $r\sim 6M$ and $位\sim 25M$, then the damping and heating effects are about 9 times larger on a Schwarzschild background than on Minkowski, and such situations occur astrophysically. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.20032v1-abstract-full').style.display = 'none'; document.getElementById('2407.20032v1-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 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.17143">arXiv:2407.17143</a> <span> [<a href="https://arxiv.org/pdf/2407.17143">pdf</a>, <a href="https://arxiv.org/format/2407.17143">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"> Astrophysical and cosmological scenarios for gravitational wave heating </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Kakkat%2C+V">Vishnu Kakkat</a>, <a href="/search/gr-qc?searchtype=author&query=Kubeka%2C+A+S">Amos S. Kubeka</a>, <a href="/search/gr-qc?searchtype=author&query=Naidoo%2C+M">Monos Naidoo</a>, <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">Petrus J. van der Walt</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="2407.17143v1-abstract-short" style="display: inline;"> Gravitational waves (GWs) passing through a viscous shell of matter are expected to be damped resulting in an increase in the temperature of the fluid as energy is transferred to it from the GWs. In previous work we constructed a model for this process, obtaining an expression for the temperature distribution inside the shell, and it was shown that the temperature increase can be astrophysically s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.17143v1-abstract-full').style.display = 'inline'; document.getElementById('2407.17143v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.17143v1-abstract-full" style="display: none;"> Gravitational waves (GWs) passing through a viscous shell of matter are expected to be damped resulting in an increase in the temperature of the fluid as energy is transferred to it from the GWs. In previous work we constructed a model for this process, obtaining an expression for the temperature distribution inside the shell, and it was shown that the temperature increase can be astrophysically significant. In this paper we extend the analysis to GW heating and damping following a binary neutron star merger, GW heating during a core-collapse supernova, and primordial gravitational waves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.17143v1-abstract-full').style.display = 'none'; document.getElementById('2407.17143v1-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> 24 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.06636">arXiv:2407.06636</a> <span> [<a href="https://arxiv.org/pdf/2407.06636">pdf</a>, <a href="https://arxiv.org/format/2407.06636">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.111.044002">10.1103/PhysRevD.111.044002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Mongwane%2C+B">Bishop Mongwane</a>, <a href="/search/gr-qc?searchtype=author&query=Nkele%2C+S">Sipho Nkele</a>, <a href="/search/gr-qc?searchtype=author&query=Duniya%2C+D+G+A">Didam G. A. Duniya</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="2407.06636v2-abstract-short" style="display: inline;"> Studies of quasinormal modes (QNMs) of black holes have a long and well established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler and Zerilli. In this work we study linearized perturbations of a Schwarzschild black hole using the Characteristic formulation of numerical relativity, with an emphasis on the computation of QNMs. Wit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.06636v2-abstract-full').style.display = 'inline'; document.getElementById('2407.06636v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.06636v2-abstract-full" style="display: none;"> Studies of quasinormal modes (QNMs) of black holes have a long and well established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler and Zerilli. In this work we study linearized perturbations of a Schwarzschild black hole using the Characteristic formulation of numerical relativity, with an emphasis on the computation of QNMs. Within this formalism, the master equation describing gravitational perturbations is known to satisfy a fourth order differential equation. We analyse the singular points of this master equation, and obtain series solutions whose coefficients are given by three term recurrence relations, from which Leaver's continued fraction method can be applied. Using this technique, we recover the standard Schwarzschild quasinormal modes. In addition, we find that imposing purely outgoing boundary conditions, a natural feature of the Bondi-Sachs framework, leads to the recovery of the algebraically special mode. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.06636v2-abstract-full').style.display = 'none'; document.getElementById('2407.06636v2-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 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </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, 2 figures, published in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 111, 044002 (2025) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.07743">arXiv:2405.07743</a> <span> [<a href="https://arxiv.org/pdf/2405.07743">pdf</a>, <a href="https://arxiv.org/format/2405.07743">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> <p class="title is-5 mathjax"> The interaction of gravitational waves with matter </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Kakkat%2C+V">Vishnu Kakkat</a>, <a href="/search/gr-qc?searchtype=author&query=Kubeka%2C+A+S">Amos S. Kubeka</a>, <a href="/search/gr-qc?searchtype=author&query=Naidoo%2C+M">Monos Naidoo</a>, <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">Petrus J. van der Walt</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="2405.07743v2-abstract-short" style="display: inline;"> It is well-known that gravitational waves undergo no absorption or dissipation when traversing through a perfect fluid. However, in the presence of a viscous fluid, GWs transfer energy to the fluid medium. In this paper, we present a review of our recent series of results regarding the interaction between gravitational waves and surrounding matter. Additionally, we examine the impact of a viscous… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.07743v2-abstract-full').style.display = 'inline'; document.getElementById('2405.07743v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.07743v2-abstract-full" style="display: none;"> It is well-known that gravitational waves undergo no absorption or dissipation when traversing through a perfect fluid. However, in the presence of a viscous fluid, GWs transfer energy to the fluid medium. In this paper, we present a review of our recent series of results regarding the interaction between gravitational waves and surrounding matter. Additionally, we examine the impact of a viscous fluid shell on gravitational wave propagation, focusing particularly on GW damping and GW heating. Furthermore, we explore the significance of these effects in various astrophysical scenarios such as core-collapse Supernovae and primordial gravitational waves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.07743v2-abstract-full').style.display = 'none'; document.getElementById('2405.07743v2-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 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </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">Essay written for the Gravity Research Foundation 2024 Awards for Essays on Gravitation</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.01615">arXiv:2308.01615</a> <span> [<a href="https://arxiv.org/pdf/2308.01615">pdf</a>, <a href="https://arxiv.org/format/2308.01615">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.109.024013">10.1103/PhysRevD.109.024013 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gravitational Wave Heating </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Kakkat%2C+V">Vishnu Kakkat</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Kubeka%2C+A+S">Amos S. Kubeka</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="2308.01615v2-abstract-short" style="display: inline;"> It was shown in previous work that when a gravitational wave (GW) passes through a viscous shell of matter the magnitude of the GW will be damped and there are astrohysical circumstances in which the damping is almost complete. The energy transfer from the GWs to the fluid will increase its temperature. We construct a model for this process and obtain an expression for the temperature distribution… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.01615v2-abstract-full').style.display = 'inline'; document.getElementById('2308.01615v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.01615v2-abstract-full" style="display: none;"> It was shown in previous work that when a gravitational wave (GW) passes through a viscous shell of matter the magnitude of the GW will be damped and there are astrohysical circumstances in which the damping is almost complete. The energy transfer from the GWs to the fluid will increase its temperature. We construct a model for this process and obtain an expression for the temperature distribution inside the shell in terms of spherical harmonics. Further, it is shown that this effect is astrophysically significant: a model problem is constructed for which the temperature increase is of order $10^6{}^\circ$K. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.01615v2-abstract-full').style.display = 'none'; document.getElementById('2308.01615v2-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 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review D, 109, 024013 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.13010">arXiv:2306.13010</a> <span> [<a href="https://arxiv.org/pdf/2306.13010">pdf</a>, <a href="https://arxiv.org/format/2306.13010">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.108.104033">10.1103/PhysRevD.108.104033 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Numerical convergence of model Cauchy-characteristic extraction and matching </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Giannakopoulos%2C+T">Thanasis Giannakopoulos</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Hilditch%2C+D">David Hilditch</a>, <a href="/search/gr-qc?searchtype=author&query=Pollney%2C+D">Denis Pollney</a>, <a href="/search/gr-qc?searchtype=author&query=Zilh%C3%A3o%2C+M">Miguel Zilh茫o</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="2306.13010v2-abstract-short" style="display: inline;"> Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers. Cauchy-characteristic extraction and matching are methods to compute gravitational waves at null infinity, a mathematical idealization of detector location, from n… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.13010v2-abstract-full').style.display = 'inline'; document.getElementById('2306.13010v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.13010v2-abstract-full" style="display: none;"> Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers. Cauchy-characteristic extraction and matching are methods to compute gravitational waves at null infinity, a mathematical idealization of detector location, from numerical relativity simulations. Both methods can in principle contribute to modeling by providing highly accurate gravitational waveforms. An underappreciated subtlety in realizing this potential is posed by the (mere) weak hyperbolicity of the particular PDE systems solved in the characteristic formulation of the Einstein field equations. This shortcoming results from the popular choice of Bondi-like coordinates. So motivated, we construct toy models that capture that PDE structure and study Cauchy-characteristic extraction and matching with them. Where possible we provide energy estimates for their solutions and perform careful numerical norm convergence tests to demonstrate the effect of weak hyperbolicity on Cauchy-characteristic extraction and matching. Our findings strongly indicate that, as currently formulated, Cauchy-characteristic matching for the Einstein field equations would provide solutions that are, at best, convergent at an order lower than expected for the numerical method, and may be unstable. In contrast, under certain conditions, the extraction method can provide properly convergent solutions. Establishing however that these conditions hold for the aforementioned characteristic formulations is still an open problem. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.13010v2-abstract-full').style.display = 'none'; document.getElementById('2306.13010v2-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, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </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">20 pages, 11 figures, 2 tables, data and code can be found at http://dx.doi.org/10.5281/zenodo.7981429 and https://github.com/ThanasisGiannakopoulos/model_CCE_CCM_public, updated to match published version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.15103">arXiv:2206.15103</a> <span> [<a href="https://arxiv.org/pdf/2206.15103">pdf</a>, <a href="https://arxiv.org/format/2206.15103">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"> Effect of a viscous fluid shell on the propagation of gravitational waves </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">Petrus J. van der Walt</a>, <a href="/search/gr-qc?searchtype=author&query=Naidoo%2C+M">Monos Naidoo</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="2206.15103v2-abstract-short" style="display: inline;"> In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.15103v2-abstract-full').style.display = 'inline'; document.getElementById('2206.15103v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.15103v2-abstract-full" style="display: none;"> In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here, we start with the (previously found) velocity field of the matter, and use it to determine the shear tensor of the fluid flow. Then, for a viscous fluid, the energy dissipated is calculated, leading to an equation for GW damping. It is found that the damping effect agrees with previous results when the wavelength $位$ is much smaller than the radius $r_i$ of the matter shell; but if $位\gg r_i$, then the damping effect is greatly increased. Next, the paper discusses an astrophysical application, CCSNe. There are several different physical processes that generate GWs, and many models have been presented in the literature. The damping effect thus needs to be evaluated with each of the parameters $位,r_i$ and the coefficient of shear viscosity $畏$, having a range of values. It is found that in most cases there will be significant damping, and in some cases that it is almost complete. We also consider the effect of viscous damping on primordial gravitational waves (pGWs) generated during inflation in the early Universe. Two cases are investigated where the wavelength is either much shorter than the shell radii or much longer; we find that there are conditions that will produce significant damping, to the extent that the waves would not be detectable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.15103v2-abstract-full').style.display = 'none'; document.getElementById('2206.15103v2-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, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.14794">arXiv:2111.14794</a> <span> [<a href="https://arxiv.org/pdf/2111.14794">pdf</a>, <a href="https://arxiv.org/format/2111.14794">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.105.084055">10.1103/PhysRevD.105.084055 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gauge structure of the Einstein field equations in Bondi-like coordinates </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Giannakopoulos%2C+T">Thanasis Giannakopoulos</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Hilditch%2C+D">David Hilditch</a>, <a href="/search/gr-qc?searchtype=author&query=Pollney%2C+D">Denis Pollney</a>, <a href="/search/gr-qc?searchtype=author&query=Zilhao%2C+M">Miguel Zilhao</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="2111.14794v2-abstract-short" style="display: inline;"> The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype formulations of this type are only weakly hyperbolic. Presently we examine the root cause of this result. In a linear analysis we identify the gauge, constraint and ph… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.14794v2-abstract-full').style.display = 'inline'; document.getElementById('2111.14794v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.14794v2-abstract-full" style="display: none;"> The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype formulations of this type are only weakly hyperbolic. Presently we examine the root cause of this result. In a linear analysis we identify the gauge, constraint and physical blocks in the principal part of the Einstein field equations in such a gauge, and show that the subsystem related to the gauge variables is only weakly hyperbolic. Weak hyperbolicity of the full system follows as a consequence in many cases. We demonstrate this explicitly in specific examples, and thus argue that Bondi-like gauges result in weakly hyperbolic free evolution systems under quite general conditions. Consequently the characteristic initial (boundary) value problem of GR in these gauges is rendered ill-posed in the simplest norms one would like to employ. The possibility of finding good alternative norms, in which well-posedness is achieved, is discussed. So motivated, we present numerical convergence tests with an implementation of full GR which demonstrate the effect of weak hyperbolicity in practice. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.14794v2-abstract-full').style.display = 'none'; document.getElementById('2111.14794v2-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 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">23 pages, 3 figures, ancillary files, data and more supplemental material at 10.5281/zenodo.5618007, updated 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> Phys. Rev. D 105, 084055 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.07675">arXiv:2103.07675</a> <span> [<a href="https://arxiv.org/pdf/2103.07675">pdf</a>, <a href="https://arxiv.org/format/2103.07675">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/10.1007/978-981-15-4702-7_1-1">10.1007/978-981-15-4702-7_1-1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Introduction to gravitational wave astronomy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="2103.07675v1-abstract-short" style="display: inline;"> This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW astronomy, from Einstein's prediction of GWs in 1916 to the first direct detection in 2015. It presents the theory of linearized perturbations about Minkowski spa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.07675v1-abstract-full').style.display = 'inline'; document.getElementById('2103.07675v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.07675v1-abstract-full" style="display: none;"> This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW astronomy, from Einstein's prediction of GWs in 1916 to the first direct detection in 2015. It presents the theory of linearized perturbations about Minkowski spacetime of Einstein's equations, and shows how gauge transformations reduce the problem to the standard wave equation with two degrees of freedom, or polarizations, $h_+,h_\times$. We derive the quadrupole formula, which relates the motion of matter in a source region to the far GW field. It is shown that GWs carry energy, as well as linear and angular momentum, away from a source. The GW field of an orbiting circular binary is found; and properties of the evolution of the binary including rate of inspiral and time to coalescence, are calculated. A brief review is given of existing and proposed GW detectors, and of how to estimate source parameters in LIGO or Virgo data of a GW event. The contributions that GW observations have already made to physics, astrophysics and cosmology are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.07675v1-abstract-full').style.display = 'none'; document.getElementById('2103.07675v1-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, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">To be published in "Handbook of Gravitational Wave Astronomy"</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.00060">arXiv:2102.00060</a> <span> [<a href="https://arxiv.org/pdf/2102.00060">pdf</a>, <a href="https://arxiv.org/format/2102.00060">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/10.1007/s10714-021-02841-z">10.1007/s10714-021-02841-z <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Modifications to the signal from a gravitational wave event due to a surrounding shell of matter </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Naidoo%2C+M">Monos Naidoo</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">Petrus J van der Walt</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="2102.00060v1-abstract-short" style="display: inline;"> In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these results to astrophysical scenarios. Firstly, it is shown that GW echoes that are claimed to be present in LIGO data of certain events, could not have been caused by a matter shell. However, it is also shown that there are scenarios in whic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.00060v1-abstract-full').style.display = 'inline'; document.getElementById('2102.00060v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.00060v1-abstract-full" style="display: none;"> In previous work, we established theoretical results concerning the effect of matter shells surrounding a gravitational wave (GW) source, and we now apply these results to astrophysical scenarios. Firstly, it is shown that GW echoes that are claimed to be present in LIGO data of certain events, could not have been caused by a matter shell. However, it is also shown that there are scenarios in which matter shells could make modifications of order a few percent to a GW signal; these scenarios include binary black hole mergers, binary neutron star mergers, and core collapse supernovae. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.00060v1-abstract-full').style.display = 'none'; document.getElementById('2102.00060v1-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 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">13 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gen. Rel. Grav. (2021) 53:77 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.08289">arXiv:1912.08289</a> <span> [<a href="https://arxiv.org/pdf/1912.08289">pdf</a>, <a href="https://arxiv.org/format/1912.08289">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/10.1007/s10714-020-02740-9">10.1007/s10714-020-02740-9 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Effect of a low density dust shell on the propagation of gravitational waves </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">Petrus J. van der Walt</a>, <a href="/search/gr-qc?searchtype=author&query=Naidoo%2C+M">Monos Naidoo</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="1912.08289v2-abstract-short" style="display: inline;"> Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy bei… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.08289v2-abstract-full').style.display = 'inline'; document.getElementById('1912.08289v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.08289v2-abstract-full" style="display: none;"> Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.08289v2-abstract-full').style.display = 'none'; document.getElementById('1912.08289v2-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 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gen. Rel. Grav., 52:92 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1606.02532">arXiv:1606.02532</a> <span> [<a href="https://arxiv.org/pdf/1606.02532">pdf</a>, <a href="https://arxiv.org/format/1606.02532">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/10.1007/s41114-016-0001-9">10.1007/s41114-016-0001-9 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Extraction of Gravitational Waves in Numerical Relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Rezzolla%2C+L">Luciano Rezzolla</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="1606.02532v2-abstract-short" style="display: inline;"> A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.02532v2-abstract-full').style.display = 'inline'; document.getElementById('1606.02532v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1606.02532v2-abstract-full" style="display: none;"> A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.02532v2-abstract-full').style.display = 'none'; document.getElementById('1606.02532v2-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 July, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">110 pages, matches version accepted in Living Reviews of Relativity; supplementary macro files available in the source tar</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.07362">arXiv:1601.07362</a> <span> [<a href="https://arxiv.org/pdf/1601.07362">pdf</a>, <a href="https://arxiv.org/format/1601.07362">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> </div> <p class="title is-5 mathjax"> Numerically reconstructing the geometry of the Universe from data </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bester%2C+H+L">Hertzog L. Bester</a>, <a href="/search/gr-qc?searchtype=author&query=Larena%2C+J">Julien Larena</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="1601.07362v2-abstract-short" style="display: inline;"> We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as al… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.07362v2-abstract-full').style.display = 'inline'; document.getElementById('1601.07362v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.07362v2-abstract-full" style="display: none;"> We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time Universe cannot be ruled out by these data alone. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.07362v2-abstract-full').style.display = 'none'; document.getElementById('1601.07362v2-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 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 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">6 pages, 2 figures, contribution to 14th 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/1512.05663">arXiv:1512.05663</a> <span> [<a href="https://arxiv.org/pdf/1512.05663">pdf</a>, <a href="https://arxiv.org/ps/1512.05663">ps</a>, <a href="https://arxiv.org/format/1512.05663">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.93.044025">10.1103/PhysRevD.93.044025 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gravitational waves in a de Sitter universe </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="1512.05663v2-abstract-short" style="display: inline;"> The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1512.05663v2-abstract-full').style.display = 'inline'; document.getElementById('1512.05663v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1512.05663v2-abstract-full" style="display: none;"> The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1512.05663v2-abstract-full').style.display = 'none'; document.getElementById('1512.05663v2-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, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 December, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">9 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, 044025 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1506.01591">arXiv:1506.01591</a> <span> [<a href="https://arxiv.org/pdf/1506.01591">pdf</a>, <a href="https://arxiv.org/format/1506.01591">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cosmology and Nongalactic Astrophysics">astro-ph.CO</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/10.1093/mnras/stv1672">10.1093/mnras/stv1672 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards the geometry of the universe from data </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bester%2C+H+L">Hertzog L. Bester</a>, <a href="/search/gr-qc?searchtype=author&query=Larena%2C+J">Julien Larena</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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="1506.01591v3-abstract-short" style="display: inline;"> We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.01591v3-abstract-full').style.display = 'inline'; document.getElementById('1506.01591v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1506.01591v3-abstract-full" style="display: none;"> We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and age data to constrain the geometry of the universe up to a redshift of $z = 1.75$. We show that, although current data are perfectly compatible with homogeneous models of the universe, simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time universe cannot yet be ruled out. In doing so we reconstruct the density of cold dark matter out to $z = 1.75$ and derive constraints on the metric components when the universe was 10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.01591v3-abstract-full').style.display = 'none'; document.getElementById('1506.01591v3-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 September, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">15 pages, 8 figures. Matches published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Monthly Notices of the Royal Astronomical Society 2015 453 (3): 2364-2377 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1308.1521">arXiv:1308.1521</a> <span> [<a href="https://arxiv.org/pdf/1308.1521">pdf</a>, <a href="https://arxiv.org/format/1308.1521">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/10.1007/s10714-013-1643-5">10.1007/s10714-013-1643-5 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The gravitational wave strain in the characteristic formalism of numerical relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Reisswig%2C+C">Christian Reisswig</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="1308.1521v2-abstract-short" style="display: inline;"> The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the PITT code within the Einstein Toolkit. Using the new strain formula, we show that artificial non-linear drifts inherent in time integrated waveforms can be reduced… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.1521v2-abstract-full').style.display = 'inline'; document.getElementById('1308.1521v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1308.1521v2-abstract-full" style="display: none;"> The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the PITT code within the Einstein Toolkit. Using the new strain formula, we show that artificial non-linear drifts inherent in time integrated waveforms can be reduced for the case of a binary black hole merger configuration. For the test case of a rapidly spinning stellar core collapse model, however, we find that the drift must have different roots. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.1521v2-abstract-full').style.display = 'none'; document.getElementById('1308.1521v2-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 December, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">9 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> General Relativity and Gravitation (2014) 46:1643 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1208.3891">arXiv:1208.3891</a> <span> [<a href="https://arxiv.org/pdf/1208.3891">pdf</a>, <a href="https://arxiv.org/format/1208.3891">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/10.1007/s10714-013-1513-1">10.1007/s10714-013-1513-1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> General relativistic null-cone evolutions with a high-order scheme </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Reisswig%2C+C">Christian Reisswig</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Pollney%2C+D">Denis Pollney</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="1208.3891v1-abstract-short" style="display: inline;"> We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.3891v1-abstract-full').style.display = 'inline'; document.getElementById('1208.3891v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1208.3891v1-abstract-full" style="display: none;"> We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.3891v1-abstract-full').style.display = 'none'; document.getElementById('1208.3891v1-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 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">24 pages, 3 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/1111.6025">arXiv:1111.6025</a> <span> [<a href="https://arxiv.org/pdf/1111.6025">pdf</a>, <a href="https://arxiv.org/ps/1111.6025">ps</a>, <a href="https://arxiv.org/format/1111.6025">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.85.044016">10.1103/PhysRevD.85.044016 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">P. J. van der Walt</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</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="1111.6025v1-abstract-short" style="display: inline;"> The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.6025v1-abstract-full').style.display = 'inline'; document.getElementById('1111.6025v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1111.6025v1-abstract-full" style="display: none;"> The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use of information causally connected to an observer. However, the diameter distance, which is used as a radial coordinate, limits the model's cosmological application to the region prior to the PNC refocussing. This is because after refocussing, the diameter distance ceases to be a unique measure of distance. This paper addresses the problem by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced by an affine parameter. A model is derived from this metric and it is then shown how an existing numerical scheme can be adapted for simulation of cosmological PNC behaviour. Numerical calculations on this model are found to have the same stability and convergence properties as the standard characteristic formalism. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.6025v1-abstract-full').style.display = 'none'; document.getElementById('1111.6025v1-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 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">18 pages, 9 figures, 1 Table. arXiv admin note: some text overlap with arXiv:some 1007.3189</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1007.3189">arXiv:1007.3189</a> <span> [<a href="https://arxiv.org/pdf/1007.3189">pdf</a>, <a href="https://arxiv.org/ps/1007.3189">ps</a>, <a href="https://arxiv.org/format/1007.3189">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.82.084001">10.1103/PhysRevD.82.084001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Observational cosmology using characteristic numerical relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=van+der+Walt%2C+P+J">P. J. van der Walt</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</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="1007.3189v1-abstract-short" style="display: inline;"> The characteristic formalism in numerical relativity, which has been developed to study gravitational waves, and the observer metric approach in observational cosmology both make use of coordinate systems based on null cones. In this paper, these coordinate systems are compared and it is then demonstrated how characteristic numerical relativity can be used to investigate problems in observational… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1007.3189v1-abstract-full').style.display = 'inline'; document.getElementById('1007.3189v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1007.3189v1-abstract-full" style="display: none;"> The characteristic formalism in numerical relativity, which has been developed to study gravitational waves, and the observer metric approach in observational cosmology both make use of coordinate systems based on null cones. In this paper, these coordinate systems are compared and it is then demonstrated how characteristic numerical relativity can be used to investigate problems in observational cosmology. In a numerical experiment using the characteristic formalism, it is shown how the historical evolution of a LTB universe compares to that of the $螞$CDM model given identical observational data on a local observer's past null cone. It is demonstrated that, at an earlier epoch of the LTB model, the observational data would not be consistent with that of the $螞$CDM model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1007.3189v1-abstract-full').style.display = 'none'; document.getElementById('1007.3189v1-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 July, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D82:084001,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0912.1285">arXiv:0912.1285</a> <span> [<a href="https://arxiv.org/pdf/0912.1285">pdf</a>, <a href="https://arxiv.org/format/0912.1285">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="Cosmology and Nongalactic Astrophysics">astro-ph.CO</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/10.1088/0264-9381/27/7/075014">10.1088/0264-9381/27/7/075014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Reisswig%2C+C">C. Reisswig</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Pollney%2C+D">D. Pollney</a>, <a href="/search/gr-qc?searchtype=author&query=Szilagyi%2C+B">B. Szilagyi</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="0912.1285v2-abstract-short" style="display: inline;"> The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction techni… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0912.1285v2-abstract-full').style.display = 'inline'; document.getElementById('0912.1285v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0912.1285v2-abstract-full" style="display: none;"> The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $\scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0912.1285v2-abstract-full').style.display = 'none'; document.getElementById('0912.1285v2-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> 10 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 December, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">41 pages, 8 figures, 2 tables, added references, fixed typos. Version matches 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. 27 075014 (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0907.2637">arXiv:0907.2637</a> <span> [<a href="https://arxiv.org/pdf/0907.2637">pdf</a>, <a href="https://arxiv.org/ps/0907.2637">ps</a>, <a href="https://arxiv.org/format/0907.2637">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.103.221101">10.1103/PhysRevLett.103.221101 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Unambiguous determination of gravitational waveforms from binary black hole mergers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Reisswig%2C+C">C. Reisswig</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Pollney%2C+D">D. Pollney</a>, <a href="/search/gr-qc?searchtype=author&query=Szilagyi%2C+B">B. Szilagyi</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="0907.2637v3-abstract-short" style="display: inline;"> Gravitational radiation is properly defined only at future null infinity ($\scri$), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at $\scri$ for the inspiral and merger of two equal mass non-spinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. T… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.2637v3-abstract-full').style.display = 'inline'; document.getElementById('0907.2637v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0907.2637v3-abstract-full" style="display: none;"> Gravitational radiation is properly defined only at future null infinity ($\scri$), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at $\scri$ for the inspiral and merger of two equal mass non-spinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose, and can be applied to calculate the gravitational radiation, at $\scri$, given data at a finite radius calculated in another computation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.2637v3-abstract-full').style.display = 'none'; document.getElementById('0907.2637v3-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> 8 January, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 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">4 pages, 3 figures, 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.Lett.103:221101,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0907.1882">arXiv:0907.1882</a> <span> [<a href="https://arxiv.org/pdf/0907.1882">pdf</a>, <a href="https://arxiv.org/ps/0907.1882">ps</a>, <a href="https://arxiv.org/format/0907.1882">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.80.064011">10.1103/PhysRevD.80.064011 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quasi-Normal Modes of a Schwarzschild White Hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Kubeka%2C+A+S">Amos S. Kubeka</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="0907.1882v1-abstract-short" style="display: inline;"> We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasi-normal modes, and present results for the case $\ell=2$. The values obtained are different to those of a Schwarzschild black hole, and we interpret them as quasi-normal modes of a Schw… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.1882v1-abstract-full').style.display = 'inline'; document.getElementById('0907.1882v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0907.1882v1-abstract-full" style="display: none;"> We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasi-normal modes, and present results for the case $\ell=2$. The values obtained are different to those of a Schwarzschild black hole, and we interpret them as quasi-normal modes of a Schwarzschild white hole. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.1882v1-abstract-full').style.display = 'none'; document.getElementById('0907.1882v1-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> 10 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">5 pages, 4 Figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D80:064011,2009 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0808.0861">arXiv:0808.0861</a> <span> [<a href="https://arxiv.org/pdf/0808.0861">pdf</a>, <a href="https://arxiv.org/ps/0808.0861">ps</a>, <a href="https://arxiv.org/format/0808.0861">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.79.084011">10.1103/PhysRevD.79.084011 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Strategies for the Characteristic Extraction of Gravitational Waveforms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Babiuc%2C+M+C">M. C. Babiuc</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Szilagyi%2C+B">B. Szilagyi</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">J. Winicour</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="0808.0861v2-abstract-short" style="display: inline;"> We develop, test and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross-sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0808.0861v2-abstract-full').style.display = 'inline'; document.getElementById('0808.0861v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0808.0861v2-abstract-full" style="display: none;"> We develop, test and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross-sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component $唯_4$ to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the $O(1/r)$ radiative part of $唯_4$ in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0808.0861v2-abstract-full').style.display = 'none'; document.getElementById('0808.0861v2-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 September, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 August, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">26 pages, 14 figures, Published in Phys.Rev.D79:084011,2009</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D79:084011,2009 </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/0610019">arXiv:gr-qc/0610019</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0610019">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0610019">ps</a>, <a href="https://arxiv.org/format/gr-qc/0610019">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/10.1088/0264-9381/24/12/S21">10.1088/0264-9381/24/12/S21 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Numerical relativity with characteristic evolution, using six angular patches </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Reisswig%2C+C">Christian Reisswig</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Lai%2C+C+W">Chi Wai Lai</a>, <a href="/search/gr-qc?searchtype=author&query=Thornburg%2C+J">Jonathan Thornburg</a>, <a href="/search/gr-qc?searchtype=author&query=Szilagyi%2C+B">Bela Szilagyi</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/0610019v1-abstract-short" style="display: inline;"> The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing tw… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0610019v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0610019v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0610019v1-abstract-full" style="display: none;"> The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0610019v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0610019v1-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 October, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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, 5 figures, submitted to CQG (special NFNR issue)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class.Quant.Grav.24:S327-S340,2007 </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/0506077">arXiv:gr-qc/0506077</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0506077">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0506077">ps</a>, <a href="https://arxiv.org/format/gr-qc/0506077">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.73.084023">10.1103/PhysRevD.73.084023 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Numerical validation of the Kerr metric in Bondi-Sachs form </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Venter%2C+L+R">Liebrecht R. Venter</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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/0506077v1-abstract-short" style="display: inline;"> A metric representing the Kerr geometry has been obtained by Pretorius and Israel. We make a coordinate transformation on this metric, thereby bringing it into Bondi-Sachs form. In order to validate the metric, we evaluate it numerically on a regular grid of the new coordinates. The Ricci tensor is then computed, for different discretizations, and found to be convergent to zero. We also investig… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0506077v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0506077v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0506077v1-abstract-full" style="display: none;"> A metric representing the Kerr geometry has been obtained by Pretorius and Israel. We make a coordinate transformation on this metric, thereby bringing it into Bondi-Sachs form. In order to validate the metric, we evaluate it numerically on a regular grid of the new coordinates. The Ricci tensor is then computed, for different discretizations, and found to be convergent to zero. We also investigate the behaviour of the metric near the axis of symmetry and confirm regularity. Finally we investigate a Bondi-Sachs representation of the Kerr geometry reported by Fletcher and Lun; we confirm numerically that their metric is Ricci flat, but find that it has an irregular behaviour at the pole. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0506077v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0506077v1-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 June, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2005. </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</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D73:084023,2006 </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/0412080">arXiv:gr-qc/0412080</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0412080">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0412080">ps</a>, <a href="https://arxiv.org/format/gr-qc/0412080">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.72.024002">10.1103/PhysRevD.72.024002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On characteristic initial data for a star orbiting a black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">Roberto Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">Luis Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Maharaj%2C+M">Manoj Maharaj</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/0412080v1-abstract-short" style="display: inline;"> We take further steps in the development of the characteristic approach to enable handling the physical problem of a compact self-gravitating object, such as a neutron star, in close orbit around a black hole. We examine different options for setting the initial data for this problem and, in order to shed light on their physical relevance, we carry out short time evolution of this data. To this… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412080v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0412080v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0412080v1-abstract-full" style="display: none;"> We take further steps in the development of the characteristic approach to enable handling the physical problem of a compact self-gravitating object, such as a neutron star, in close orbit around a black hole. We examine different options for setting the initial data for this problem and, in order to shed light on their physical relevance, we carry out short time evolution of this data. To this end we express the matter part of the characteristic gravity code so that the hydrodynamics are in conservation form. The resulting gravity plus matter relativity code provides a starting point for more refined future efforts at longer term evolution. In the present work we find that, independently of the details of the initial gravitational data, the system quickly flushes out spurious gravitational radiation and relaxes to a quasi-equilibrium state with an approximate helical symmetry corresponding to the circular orbit of the star. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412080v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0412080v1-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 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">20 pages, 10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D72 (2005) 024002 </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/0412006">arXiv:gr-qc/0412006</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0412006">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0412006">ps</a>, <a href="https://arxiv.org/format/gr-qc/0412006">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/10.1088/0264-9381/22/12/006">10.1088/0264-9381/22/12/006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</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/0412006v2-abstract-short" style="display: inline;"> We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By performing an eigenfunction decomposition, we reduce the problem to a system of linear ordinary differential equations which we are able to solve. The solutions… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412006v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0412006v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0412006v2-abstract-full" style="display: none;"> We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By performing an eigenfunction decomposition, we reduce the problem to a system of linear ordinary differential equations which we are able to solve. The solutions are relevant to the characteristic formulation of numerical relativity: (a) as exact solutions against which computations of gravitational radiation can be compared; and (b) in formulating boundary conditions on the $r=2M$ Schwarzschild horizon. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0412006v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0412006v2-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> 10 June, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 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">Revised following referee comments</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class.Quant.Grav. 22 (2005) 2393-2406 </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/0310011">arXiv:gr-qc/0310011</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0310011">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0310011">ps</a>, <a href="https://arxiv.org/format/gr-qc/0310011">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.69.064010">10.1103/PhysRevD.69.064010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Black hole initial data from a non-conformal decomposition </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Beyer%2C+F">Florian Beyer</a>, <a href="/search/gr-qc?searchtype=author&query=Koppitz%2C+M">Michael Koppitz</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/0310011v2-abstract-short" style="display: inline;"> We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of axisymmetry, we have written a program to solve the resulting nonlinear elliptic equation. We have obtained solutions, both numerically and from a linearized a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310011v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0310011v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0310011v2-abstract-full" style="display: none;"> We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of axisymmetry, we have written a program to solve the resulting nonlinear elliptic equation. We have obtained solutions, both numerically and from a linearized analytic method, for a general perturbation of Schwarzschild. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310011v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0310011v2-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, 2004; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 October, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2003. </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, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D69 (2004) 064010 </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/0303021">arXiv:gr-qc/0303021</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0303021">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0303021">ps</a>, <a href="https://arxiv.org/format/gr-qc/0303021">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.68.024031">10.1103/PhysRevD.68.024031 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> New approach to calculating the News </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Deshingkar%2C+S+S">Shrirang S. Deshingkar</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/0303021v2-abstract-short" style="display: inline;"> We consider the problem of finding the gravitational radiation output, or news, within the context of a numerical simulation of a spacetime by means of the null-cone, or characteristic, approach to numerical relativity. We develop a method for computing the news that uses an explicit coordinate transformation to a coordinate system that satisfies the Bondi conditions. The method has been impleme… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0303021v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0303021v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0303021v2-abstract-full" style="display: none;"> We consider the problem of finding the gravitational radiation output, or news, within the context of a numerical simulation of a spacetime by means of the null-cone, or characteristic, approach to numerical relativity. We develop a method for computing the news that uses an explicit coordinate transformation to a coordinate system that satisfies the Bondi conditions. The method has been implemented computationally. We present results of applying the method to certain test problems, demonstrating second order convergence of the news to the analytic value. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0303021v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0303021v2-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 June, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 March, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2003. </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">Some additions and minor changes in presentation. Accepted for publication in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D68:024031,2003 </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/0301060">arXiv:gr-qc/0301060</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0301060">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0301060">ps</a>, <a href="https://arxiv.org/format/gr-qc/0301060">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.68.084015">10.1103/PhysRevD.68.084015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">Roberto Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Husa%2C+S">Sascha Husa</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">Luis Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/0301060v2-abstract-short" style="display: inline;"> We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a rigid body whos… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0301060v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0301060v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0301060v2-abstract-full" style="display: none;"> We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a rigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near r=9M) of a Schwarzschild black hole. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0301060v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0301060v2-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 September, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 January, 2003; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2003. </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, 9 figures, RevTeX4, to appear in Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AEI-2003-006, NSF-KITP-03-55 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D68 (2003) 084015 </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/9912030">arXiv:gr-qc/9912030</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9912030">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9912030">ps</a>, <a href="https://arxiv.org/format/gr-qc/9912030">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.62.104006">10.1103/PhysRevD.62.104006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Cauchy boundaries in linearized gravitational theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Szilagyi%2C+B">Bela Szilagyi</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">Roberto Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/9912030v2-abstract-short" style="display: inline;"> We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3+1 formulation and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912030v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9912030v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9912030v2-abstract-full" style="display: none;"> We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3+1 formulation and measure its stability properties under Dirichlet, Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9912030v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9912030v2-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 December, 2000; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 December, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 1999. </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">23 pages including 3 figures and 2 tables, revtex</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D62 (2000) 104006 </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/9901056">arXiv:gr-qc/9901056</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9901056">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9901056">ps</a>, <a href="https://arxiv.org/format/gr-qc/9901056">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.60.024005">10.1103/PhysRevD.60.024005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The incorporation of matter into characteristic numerical relativity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">R. Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">L. Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Maharaj%2C+M">M. Maharaj</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">J. Winicour</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/9901056v1-abstract-short" style="display: inline;"> A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9901056v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9901056v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9901056v1-abstract-full" style="display: none;"> A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems in black hole astrophysics. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9901056v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9901056v1-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 January, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 1999. </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 + 4 (eps) figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D60:024005,1999 </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/9809034">arXiv:gr-qc/9809034</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9809034">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9809034">ps</a>, <a href="https://arxiv.org/format/gr-qc/9809034">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.60.044005">10.1103/PhysRevD.60.044005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">Luis Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=G%C3%B3mez%2C+R">Roberto G贸mez</a>, <a href="/search/gr-qc?searchtype=author&query=Szil%C3%A1gyi%2C+B">B茅la Szil谩gyi</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/9809034v2-abstract-short" style="display: inline;"> We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9809034v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9809034v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9809034v2-abstract-full" style="display: none;"> We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9809034v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9809034v2-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 May, 1999; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 September, 1998; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 1998. </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">21 pages, 6 figures, revtex, 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. D 60, 044005 (1999) </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/9711078">arXiv:gr-qc/9711078</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9711078">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9711078">ps</a>, <a href="https://arxiv.org/format/gr-qc/9711078">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.80.2512">10.1103/PhysRevLett.80.2512 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Boosted three-dimensional black-hole evolutions with singularity excision </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Alliance%2C+T+B+B+H+G+C">The Binary Black Hole Grand Challenge Alliance</a>, <a href="/search/gr-qc?searchtype=author&query=%3A"> :</a>, <a href="/search/gr-qc?searchtype=author&query=Cook%2C+G+B">G. B. Cook</a>, <a href="/search/gr-qc?searchtype=author&query=Huq%2C+M+F">M. F. Huq</a>, <a href="/search/gr-qc?searchtype=author&query=Klasky%2C+S+A">S. A. Klasky</a>, <a href="/search/gr-qc?searchtype=author&query=Scheel%2C+M+A">M. A. Scheel</a>, <a href="/search/gr-qc?searchtype=author&query=Abrahams%2C+A+M">A. M. Abrahams</a>, <a href="/search/gr-qc?searchtype=author&query=Anderson%2C+A">A. Anderson</a>, <a href="/search/gr-qc?searchtype=author&query=Anninos%2C+P">P. Anninos</a>, <a href="/search/gr-qc?searchtype=author&query=Baumgarte%2C+T+W">T. W. Baumgarte</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Brandt%2C+S+R">S. R. Brandt</a>, <a href="/search/gr-qc?searchtype=author&query=Browne%2C+J+C">J. C. Browne</a>, <a href="/search/gr-qc?searchtype=author&query=Camarda%2C+K">K. Camarda</a>, <a href="/search/gr-qc?searchtype=author&query=Choptuik%2C+M+W">M. W. Choptuik</a>, <a href="/search/gr-qc?searchtype=author&query=Evans%2C+C+R">C. R. Evans</a>, <a href="/search/gr-qc?searchtype=author&query=Finn%2C+L+S">L. S. Finn</a>, <a href="/search/gr-qc?searchtype=author&query=Fox%2C+G+C">G. C. Fox</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">R. Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Haupt%2C+T">T. Haupt</a>, <a href="/search/gr-qc?searchtype=author&query=Kidder%2C+L+E">L. E. Kidder</a>, <a href="/search/gr-qc?searchtype=author&query=Laguna%2C+P">P. Laguna</a>, <a href="/search/gr-qc?searchtype=author&query=Landry%2C+W">W. Landry</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">L. Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Lenaghan%2C+J">J. Lenaghan</a> , et al. (21 additional authors not shown) </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/9711078v1-abstract-short" style="display: inline;"> Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on singl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9711078v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9711078v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9711078v1-abstract-full" style="display: none;"> Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of duration ~60M. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9711078v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9711078v1-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 November, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.lett.80:2512-2516,1998 </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/9711076">arXiv:gr-qc/9711076</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9711076">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9711076">ps</a>, <a href="https://arxiv.org/format/gr-qc/9711076">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.57.6113">10.1103/PhysRevD.57.6113 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Black Hole Data via a Kerr-Schild Approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Isaacson%2C+R">Richard Isaacson</a>, <a href="/search/gr-qc?searchtype=author&query=Maharaj%2C+M">Manoj Maharaj</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/9711076v1-abstract-short" style="display: inline;"> We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a simple hierarchical form which is amenable to direct numerical integration. The feasibility of this approach is demonstrated by solving analytically the probl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9711076v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9711076v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9711076v1-abstract-full" style="display: none;"> We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a simple hierarchical form which is amenable to direct numerical integration. The feasibility of this approach is demonstrated by solving analytically the problem of initial data in a perturbed Schwarzschild geometry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9711076v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9711076v1-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 November, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1997. </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, RevTeX format</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D57 (1998) 6113-6118 </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/9709082">arXiv:gr-qc/9709082</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9709082">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9709082">ps</a>, <a href="https://arxiv.org/format/gr-qc/9709082">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.80.1812">10.1103/PhysRevLett.80.1812 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gravitational wave extraction and outer boundary conditions by perturbative matching </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Alliance%2C+T+B+B+H+G+C">The Binary Black Hole Grand Challenge Alliance</a>, <a href="/search/gr-qc?searchtype=author&query=%3A"> :</a>, <a href="/search/gr-qc?searchtype=author&query=Abrahams%2C+A+M">A. M. Abrahams</a>, <a href="/search/gr-qc?searchtype=author&query=Rezzolla%2C+L">L. Rezzolla</a>, <a href="/search/gr-qc?searchtype=author&query=Rupright%2C+M+E">M. E. Rupright</a>, <a href="/search/gr-qc?searchtype=author&query=Anderson%2C+A">A. Anderson</a>, <a href="/search/gr-qc?searchtype=author&query=Anninos%2C+P">P. Anninos</a>, <a href="/search/gr-qc?searchtype=author&query=Baumgarte%2C+T+W">T. W. Baumgarte</a>, <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">N. T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=Brandt%2C+S+R">S. R. Brandt</a>, <a href="/search/gr-qc?searchtype=author&query=Browne%2C+J+C">J. C. Browne</a>, <a href="/search/gr-qc?searchtype=author&query=Camarda%2C+K">K. Camarda</a>, <a href="/search/gr-qc?searchtype=author&query=Choptuik%2C+M+W">M. W. Choptuik</a>, <a href="/search/gr-qc?searchtype=author&query=Cook%2C+G+B">G. B. Cook</a>, <a href="/search/gr-qc?searchtype=author&query=Evans%2C+C+R">C. R. Evans</a>, <a href="/search/gr-qc?searchtype=author&query=Finn%2C+L+S">L. S. Finn</a>, <a href="/search/gr-qc?searchtype=author&query=Fox%2C+G">G. Fox</a>, <a href="/search/gr-qc?searchtype=author&query=Gomez%2C+R">R. Gomez</a>, <a href="/search/gr-qc?searchtype=author&query=Haupt%2C+T">T. Haupt</a>, <a href="/search/gr-qc?searchtype=author&query=Huq%2C+M+F">M. F. Huq</a>, <a href="/search/gr-qc?searchtype=author&query=Kidder%2C+L+E">L. E. Kidder</a>, <a href="/search/gr-qc?searchtype=author&query=Klasky%2C+S">S. Klasky</a>, <a href="/search/gr-qc?searchtype=author&query=Laguna%2C+P">P. Laguna</a>, <a href="/search/gr-qc?searchtype=author&query=Landry%2C+W">W. Landry</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">L. Lehner</a> , et al. (20 additional authors not shown) </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/9709082v1-abstract-short" style="display: inline;"> We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed wi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9709082v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9709082v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9709082v1-abstract-full" style="display: none;"> We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9709082v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9709082v1-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 September, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.Lett.80:1812-1815,1998 </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/9708065">arXiv:gr-qc/9708065</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/9708065">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/9708065">ps</a>, <a href="https://arxiv.org/format/gr-qc/9708065">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.56.6298">10.1103/PhysRevD.56.6298 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> High-powered Gravitational News </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Bishop%2C+N+T">Nigel T. Bishop</a>, <a href="/search/gr-qc?searchtype=author&query=G%C3%B3mez%2C+R">Roberto G贸mez</a>, <a href="/search/gr-qc?searchtype=author&query=Lehner%2C+L">Luis Lehner</a>, <a href="/search/gr-qc?searchtype=author&query=Maharaj%2C+M">Manoj Maharaj</a>, <a href="/search/gr-qc?searchtype=author&query=Winicour%2C+J">Jeffrey Winicour</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/9708065v1-abstract-short" style="display: inline;"> We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9708065v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/9708065v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/9708065v1-abstract-full" style="display: none;"> We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard $N_{+}$ and $N_{\times}$ polarization components. The resulting code is stable and second-order convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about $10^{13}M_{\odot}/sec$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/9708065v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/9708065v1-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 August, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 1997. </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">24 pages, 4 figures. 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.D56:6298-6309,1997 </p> </li> </ol> <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 class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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