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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Hong, S"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </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/2503.08701">arXiv:2503.08701</a> <span> [<a href="https://arxiv.org/pdf/2503.08701">pdf</a>, <a href="https://arxiv.org/format/2503.08701">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/10.3390/universe11030090">10.3390/universe11030090 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Rough estimates of solar system gravitomagnetic effects in post-Newtonian gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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="2503.08701v1-abstract-short" style="display: inline;"> In order to describe properly the gravity interactions including the mass currents, in the gravitomagnetism we construct four Maxwell type gravitational equations which are shown to be analogs of the Maxwell equations in the electromagnetism. Next, exploiting the Maxwell type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.08701v1-abstract-full').style.display = 'inline'; document.getElementById('2503.08701v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.08701v1-abstract-full" style="display: none;"> In order to describe properly the gravity interactions including the mass currents, in the gravitomagnetism we construct four Maxwell type gravitational equations which are shown to be analogs of the Maxwell equations in the electromagnetism. Next, exploiting the Maxwell type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon orbiting the spinning Earth and that of the Sun and solar system planets orbiting the spinning Sun, whose phenomenological values have not been evaluated in the precedented Newtonian gravity formalisms. In the gravitomagnetism we also phenomenologically investigate the mass magnetic general relativity (GR) forces associated with the mass magnetic fields, to find that they are extremely small but non-vanishing compared to the corresponding mass electric Newtonian forces. Moreover, the directions of the mass magnetic GR forces for the solar system planets except Venus and Uranus are shown to be anti-parallel to those of their mass electric Newtonian forces. Next we investigate the mass magnetic dipole moment related with the B-ring of Saturn, to evaluate $\vec{m}_{M}(Ring)=-1.141\times 10^{4}~{\rm m^{3}~sec^{-1}}~\hat蠅$ with $\hat蠅$ being the unit vector along the axis direction of the spinning B-ring. The predicted value of $\vec{m}_{M}(Ring)$ is shown to be directly related with the Cassini data on the total mass of the rings of Saturn. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.08701v1-abstract-full').style.display = 'none'; document.getElementById('2503.08701v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Universe, 11 (2025) 90 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.13608">arXiv:2403.13608</a> <span> [<a href="https://arxiv.org/pdf/2403.13608">pdf</a>, <a href="https://arxiv.org/ps/2403.13608">ps</a>, <a href="https://arxiv.org/format/2403.13608">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/10.1088/1572-9494/ad51f0">10.1088/1572-9494/ad51f0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tidal effects based on GUP-induced effective metric </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="2403.13608v2-abstract-short" style="display: inline;"> In this paper, we study tidal forces in the Schwarzschild black hole whose metric includes explicitly a generalized uncertainty principle (GUP) effect. We also investigate interesting features of the geodesic equations and tidal effects dependent on the GUP parameter $伪$ related to a minimum length. Then, by solving geodesic deviation equations explicitly with appropriate boundary conditions, we s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.13608v2-abstract-full').style.display = 'inline'; document.getElementById('2403.13608v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.13608v2-abstract-full" style="display: none;"> In this paper, we study tidal forces in the Schwarzschild black hole whose metric includes explicitly a generalized uncertainty principle (GUP) effect. We also investigate interesting features of the geodesic equations and tidal effects dependent on the GUP parameter $伪$ related to a minimum length. Then, by solving geodesic deviation equations explicitly with appropriate boundary conditions, we show that $伪$ in the effective metric affects both the radial and angular components of the geodesic equation, particularly near the singularities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.13608v2-abstract-full').style.display = 'none'; document.getElementById('2403.13608v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">13 pages, 9 figures, version to appear in Communications in Theoretical Physics</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.07152">arXiv:2209.07152</a> <span> [<a href="https://arxiv.org/pdf/2209.07152">pdf</a>, <a href="https://arxiv.org/ps/2209.07152">ps</a>, <a href="https://arxiv.org/format/2209.07152">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/10.3390/universe9110486">10.3390/universe9110486 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> GEMS embeddings of Hayward regular black holes in massless and massive gravities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="2209.07152v2-abstract-short" style="display: inline;"> After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.07152v2-abstract-full').style.display = 'inline'; document.getElementById('2209.07152v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.07152v2-abstract-full" style="display: none;"> After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call massless. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.07152v2-abstract-full').style.display = 'none'; document.getElementById('2209.07152v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Universe 2023, 9(11), 486 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.05755">arXiv:2103.05755</a> <span> [<a href="https://arxiv.org/pdf/2103.05755">pdf</a>, <a href="https://arxiv.org/ps/2103.05755">ps</a>, <a href="https://arxiv.org/format/2103.05755">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0217732322501863">10.1142/S0217732322501863 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> GUP corrected entropy of the Schwarzschild black hole in holographic massive gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="2103.05755v2-abstract-short" style="display: inline;"> We obtain the statistical entropy of a scalar field on the Schwarzschild black hole in holographic massive gravity by considering corrections on the density of quantum states to all orders in the Planck length from a generalized uncertainty principle (GUP). As a result, we find not only the generalized Bekenstein-Hawking entropy depending on holographically massive gravitons without any artificial… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.05755v2-abstract-full').style.display = 'inline'; document.getElementById('2103.05755v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.05755v2-abstract-full" style="display: none;"> We obtain the statistical entropy of a scalar field on the Schwarzschild black hole in holographic massive gravity by considering corrections on the density of quantum states to all orders in the Planck length from a generalized uncertainty principle (GUP). As a result, we find not only the generalized Bekenstein-Hawking entropy depending on holographically massive gravitons without any artificial cutoff, but also new additional correction terms, which are proportional to surface gravity. Moreover, we also observe that all order GUP corrected entropy is improved to have smaller GUP parameter $位$ than the previous results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.05755v2-abstract-full').style.display = 'none'; document.getElementById('2103.05755v2-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> 22 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 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">12 pages, 3 figures, version to appear in MPLA</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Modern Physics Letters A, Vol.37, No.27, 2250186 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.08351">arXiv:2011.08351</a> <span> [<a href="https://arxiv.org/pdf/2011.08351">pdf</a>, <a href="https://arxiv.org/ps/2011.08351">ps</a>, <a href="https://arxiv.org/format/2011.08351">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/10.3390/universe8010015">10.3390/universe8010015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> GEMS embeddings of Schwarzschild and RN black holes in Painlev茅-Gullstrand spacetimes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="2011.08351v2-abstract-short" style="display: inline;"> Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3+1)-dimensional Schwarzschild and Reissner-Nordstr枚m (RN) black holes written by the Painlev茅-Gullstrand (PG) spacetimes, which have off-diagonal components in metrics, into (5+1)- and (5+2)-dimensional flat ones, respectively. As a result, we have shown the equivalence of the GEMS embeddings of the spacet… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.08351v2-abstract-full').style.display = 'inline'; document.getElementById('2011.08351v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.08351v2-abstract-full" style="display: none;"> Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3+1)-dimensional Schwarzschild and Reissner-Nordstr枚m (RN) black holes written by the Painlev茅-Gullstrand (PG) spacetimes, which have off-diagonal components in metrics, into (5+1)- and (5+2)-dimensional flat ones, respectively. As a result, we have shown the equivalence of the GEMS embeddings of the spacetimes with the diagonal and off-diagonal terms in metrics. Moreover, with the aid of their geodesic equations satisfying various boundary conditions in the flat embedded spacetimes, we directly obtain freely falling temperatures. We also show that freely falling temperatures in the PG spacetimes are well-defined beyond the event horizons, while they are equivalent to the Hawking temperatures, which are obtained in the original curved ones in the ranges between the horizon and the infinity. These will be helpful to study GEMS embeddings of more realistic Kerr, or rotating BTZ black holes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.08351v2-abstract-full').style.display = 'none'; document.getElementById('2011.08351v2-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 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 3 figures, version to appear in Universe</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Universe 2022, 8(1), 15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.05715">arXiv:2008.05715</a> <span> [<a href="https://arxiv.org/pdf/2008.05715">pdf</a>, <a href="https://arxiv.org/ps/2008.05715">ps</a>, <a href="https://arxiv.org/format/2008.05715">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2020.135967">10.1016/j.physletb.2020.135967 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tidal effects in Schwarzschild black hole in holographic massive gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="2008.05715v2-abstract-short" style="display: inline;"> We investigate tidal effects produced in the spacetime of Schwarzschild black hole in holographic massive gravity, which has two additional mass parameters due to massive gravitons. As a result, we have obtained that massive gravitons affect the angular component of the tidal force, while the radial component has the same form with the one in massless gravity. On the other hand, by solving the geo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.05715v2-abstract-full').style.display = 'inline'; document.getElementById('2008.05715v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.05715v2-abstract-full" style="display: none;"> We investigate tidal effects produced in the spacetime of Schwarzschild black hole in holographic massive gravity, which has two additional mass parameters due to massive gravitons. As a result, we have obtained that massive gravitons affect the angular component of the tidal force, while the radial component has the same form with the one in massless gravity. On the other hand, by solving the geodesic deviation equations, we have found that radial components of two nearby geodesics keep tightening while falling into the black hole and after passing the event horizons get abruptly infinitely stretched due to massive gravitons. However, angular components of two nearby geodesics get stretched firstly, reach a peak and then get compressed while falling into the black hole. Moreover, we have also shown that the angular components are more easily deformed near the departure position as the mass of a black hole is smaller for a fixed graviton mass. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.05715v2-abstract-full').style.display = 'none'; document.getElementById('2008.05715v2-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, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 4 figures, version to appear in PLB</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.04860">arXiv:1905.04860</a> <span> [<a href="https://arxiv.org/pdf/1905.04860">pdf</a>, <a href="https://arxiv.org/ps/1905.04860">ps</a>, <a href="https://arxiv.org/format/1905.04860">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2019.135116">10.1016/j.physletb.2019.135116 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> GEMS embeddings and freely falling temperatures of Schwarzschild(-AdS) black holes in massive gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="1905.04860v3-abstract-short" style="display: inline;"> We globally embed (3+1)-dimensional Schwarzschild and Schwarzschild-AdS black holes in massive gravity into (5+2)-dimensional flat spacetimes. Making use of embedding coordinates, we directly obtain the generalized Hawking, Unruh and freely falling temperatures in a Schwarzschild and Schwarzschild-AdS black hole due to massive graviton effects. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.04860v3-abstract-full" style="display: none;"> We globally embed (3+1)-dimensional Schwarzschild and Schwarzschild-AdS black holes in massive gravity into (5+2)-dimensional flat spacetimes. Making use of embedding coordinates, we directly obtain the generalized Hawking, Unruh and freely falling temperatures in a Schwarzschild and Schwarzschild-AdS black hole due to massive graviton effects. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.04860v3-abstract-full').style.display = 'none'; document.getElementById('1905.04860v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 7 figures, title changed, references added, version to appear in PLB. arXiv admin note: text overlap with arXiv:1812.00373</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.00373">arXiv:1812.00373</a> <span> [<a href="https://arxiv.org/pdf/1812.00373">pdf</a>, <a href="https://arxiv.org/ps/1812.00373">ps</a>, <a href="https://arxiv.org/format/1812.00373">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.99.024047">10.1103/PhysRevD.99.024047 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Local free-fall temperatures of charged BTZ black holes in massive gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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="1812.00373v3-abstract-short" style="display: inline;"> We obtain a (3+3)-dimensional global flat embedding of the generalized (2+1) charged Ba帽ados-Teitelboim-Zanelli black holes in massive gravity. We also study the local free-fall temperatures for freely falling observers starting from rest and investigate the effect of the charge and graviton mass in free-fall temperatures. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.00373v3-abstract-full" style="display: none;"> We obtain a (3+3)-dimensional global flat embedding of the generalized (2+1) charged Ba帽ados-Teitelboim-Zanelli black holes in massive gravity. We also study the local free-fall temperatures for freely falling observers starting from rest and investigate the effect of the charge and graviton mass in free-fall temperatures. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.00373v3-abstract-full').style.display = 'none'; document.getElementById('1812.00373v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 7 figures, minor changes to match the 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 99, 024047 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1407.3420">arXiv:1407.3420</a> <span> [<a href="https://arxiv.org/pdf/1407.3420">pdf</a>, <a href="https://arxiv.org/format/1407.3420">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"> Photon size in higher dimensional phantom cosmology </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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="1407.3420v3-abstract-short" style="display: inline;"> We study a higher dimensional cosmology with phantom field associated with a negative kinetic term. Assuming that the universe possesses the phantom field defined in $D$ dimensional spacetime, we investigate in detail the solutions involved in the higher dimensional phantom cosmology, to explicitly predict photon size and phantom field strength at present in nature. To be specific, we find that th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.3420v3-abstract-full').style.display = 'inline'; document.getElementById('1407.3420v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1407.3420v3-abstract-full" style="display: none;"> We study a higher dimensional cosmology with phantom field associated with a negative kinetic term. Assuming that the universe possesses the phantom field defined in $D$ dimensional spacetime, we investigate in detail the solutions involved in the higher dimensional phantom cosmology, to explicitly predict photon size and phantom field strength at present in nature. To be specific, we find that the photon size decreases drastically at the early stage of the universe after the Big Bang. Next we explicitly demonstrate the dependences of the photon size, universe size and phantom field strength on the spacetime dimensionality $D$. We observe that the size of the universe undergoes stiff explosion with different types of slope depending on $D$. Moreover the scale factor of the universe at present is shown to approach to a saturated value, which is independent of $D$ and is the same as that in the $D=4$ Friedmann-Robertson-Walker cosmology. The photon size and phantom field strength in the greater dimensionality are also shown to be larger and lower than those in the smaller one, respectively. Next the photon size at present $b_{*}$ in $D=5$ is numerically shown to be extremely small, namely $b_{*}=6.08\times 10^{-216}$ cm, comparing to $b_{*}=1.56\times 10^{-63}$ cm in $D=10$. In contrast, the phantom field strength at present $蟽_{*}$ is shown to be relatively large $蟽_{*}=4.72\times 10^{24}$ (dyne$)^{1/2}$ in $D=5$, comparing to $蟽_{*}=1.39\times 10^{22}$ (dyne$)^{1/2}$ in $D=10$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.3420v3-abstract-full').style.display = 'none'; document.getElementById('1407.3420v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 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/1406.6107">arXiv:1406.6107</a> <span> [<a href="https://arxiv.org/pdf/1406.6107">pdf</a>, <a href="https://arxiv.org/ps/1406.6107">ps</a>, <a href="https://arxiv.org/format/1406.6107">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"> Higher dimensional flat embedding of Taub-NUT-AdS spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1406.6107v2-abstract-short" style="display: inline;"> We construct a global flat embedding structure of a Taub-NUT-AdS spacetime to yield a (6+5)-dimensional novel global embedding Minkowski spacetime. We also investigate Taub-NUT, Schwarzschild-AdS and Schwarzschild limits of the global embedding by exploiting parameter reduction scheme. In particular, we observe in the vanishing monopole strength limit of the Taub-NUT-AdS that the parameter reducti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.6107v2-abstract-full').style.display = 'inline'; document.getElementById('1406.6107v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1406.6107v2-abstract-full" style="display: none;"> We construct a global flat embedding structure of a Taub-NUT-AdS spacetime to yield a (6+5)-dimensional novel global embedding Minkowski spacetime. We also investigate Taub-NUT, Schwarzschild-AdS and Schwarzschild limits of the global embedding by exploiting parameter reduction scheme. In particular, we observe in the vanishing monopole strength limit of the Taub-NUT-AdS that the parameter reduction is not smoothly applicable to the Schwarzschild-AdS, due to the presence of imaginary roots of its lapse function associated with event horizon. Moreover, reductions from the Taub-NUT-AdS and Schwarzschild-AdS to Taub-NUT and Schwarzschild, respectively, are successfully performed. Finally, we construct the global embedding Minkowski spacetimes for the patches inside the event horizons of the Taub-NUT-AdS and its extended manifolds. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.6107v2-abstract-full').style.display = 'none'; document.getElementById('1406.6107v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 February, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1406.1591">arXiv:1406.1591</a> <span> [<a href="https://arxiv.org/pdf/1406.1591">pdf</a>, <a href="https://arxiv.org/ps/1406.1591">ps</a>, <a href="https://arxiv.org/format/1406.1591">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"> Interior properties of five-dimensional Schwarzschild black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1406.1591v1-abstract-short" style="display: inline;"> We investigate inner structure of Schwarzschild black hole on a five-dimensional spacetime S^3xR^2. To do this, we exploit a f眉nfbein scheme. In particular, we construct an equation of state of hydrostatic equilibrium for the five-dimensional Schwarzschild black hole, which is a five-dimensional version of the Tolman-Oppenheimer-Volkoff equation on four-dimensional manifold. We also investigate un… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.1591v1-abstract-full').style.display = 'inline'; document.getElementById('1406.1591v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1406.1591v1-abstract-full" style="display: none;"> We investigate inner structure of Schwarzschild black hole on a five-dimensional spacetime S^3xR^2. To do this, we exploit a f眉nfbein scheme. In particular, we construct an equation of state of hydrostatic equilibrium for the five-dimensional Schwarzschild black hole, which is a five-dimensional version of the Tolman-Oppenheimer-Volkoff equation on four-dimensional manifold. We also investigate uniform density interior configuration of the five-dimensional black hole which consists of incompressible fluid of density, to find a general relativistic expression for pressure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1406.1591v1-abstract-full').style.display = 'none'; document.getElementById('1406.1591v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 June, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1309.2177">arXiv:1309.2177</a> <span> [<a href="https://arxiv.org/pdf/1309.2177">pdf</a>, <a href="https://arxiv.org/ps/1309.2177">ps</a>, <a href="https://arxiv.org/format/1309.2177">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/s10714-014-1781-4">10.1007/s10714-014-1781-4 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Warp products and (2+1) dimensional spacetimes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yeji Kim</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="1309.2177v2-abstract-short" style="display: inline;"> We investigate the geometrical aspects of the extended (2+1) dimensional Banados-Teitelboim-Zanelli spacetimes in the multiply warped product scheme. To do this, we analyze the interior physical properties by constructing the explicit warp functions in these regions. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1309.2177v2-abstract-full" style="display: none;"> We investigate the geometrical aspects of the extended (2+1) dimensional Banados-Teitelboim-Zanelli spacetimes in the multiply warped product scheme. To do this, we analyze the interior physical properties by constructing the explicit warp functions in these regions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1309.2177v2-abstract-full').style.display = 'none'; document.getElementById('1309.2177v2-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 August, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">14 pages, to appear in General Relativity and 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/1301.6353">arXiv:1301.6353</a> <span> [<a href="https://arxiv.org/pdf/1301.6353">pdf</a>, <a href="https://arxiv.org/ps/1301.6353">ps</a>, <a href="https://arxiv.org/format/1301.6353">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/10.3938/jkps.64.1928">10.3938/jkps.64.1928 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Geometrical and hydrodynamic aspects of five-dimensional Schwarzschild black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.6353v1-abstract-short" style="display: inline;"> Exploiting the five-dimensional Schwarzschild black hole, we study the geometrical natures of the higher dimensional black hole to yield the (6+1) dimensional global embedding Minkowski space structure. We next obtain the Hawking temperature on this five-dimensional manifold, whose result is different from the four-dimensional one. On the contrary, the radial component of the Einstein equation for… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6353v1-abstract-full').style.display = 'inline'; document.getElementById('1301.6353v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.6353v1-abstract-full" style="display: none;"> Exploiting the five-dimensional Schwarzschild black hole, we study the geometrical natures of the higher dimensional black hole to yield the (6+1) dimensional global embedding Minkowski space structure. We next obtain the Hawking temperature on this five-dimensional manifold, whose result is different from the four-dimensional one. On the contrary, the radial component of the Einstein equation for the massive particles or photons on the five-dimensional spacetime is shown to have the same form as the four-dimensional black hole one. Moreover, we construct the effective potential on equatorial plane of the restricted three-brane to investigate the behavior of the particles or photons on this restricted brane. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6353v1-abstract-full').style.display = 'none'; document.getElementById('1301.6353v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1209.4563">arXiv:1209.4563</a> <span> [<a href="https://arxiv.org/pdf/1209.4563">pdf</a>, <a href="https://arxiv.org/ps/1209.4563">ps</a>, <a href="https://arxiv.org/format/1209.4563">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0217732316502047">10.1142/S0217732316502047 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Global embeddings and hydrodynamic properties of Kerr black hole </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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="1209.4563v4-abstract-short" style="display: inline;"> In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons, to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.4563v4-abstract-full').style.display = 'inline'; document.getElementById('1209.4563v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1209.4563v4-abstract-full" style="display: none;"> In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons, to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies we study the black holes GRO~J1655-40 and 4U~1543-47, to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of $1.0~ly$ around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9+3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane we investigate the warp products of the Kerr spacetime. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1209.4563v4-abstract-full').style.display = 'none'; document.getElementById('1209.4563v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 September, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">10 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Mod. Phys. Lett. A, Vol. 31, No. 35 (2016) 1650204 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1108.5886">arXiv:1108.5886</a> <span> [<a href="https://arxiv.org/pdf/1108.5886">pdf</a>, <a href="https://arxiv.org/ps/1108.5886">ps</a>, <a href="https://arxiv.org/format/1108.5886">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0218271812500629">10.1142/S0218271812500629 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Possibility of Inflation in Asymptotically Safe Gravity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S+E">Sungwook E. Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Lee%2C+Y+J">Young Jae Lee</a>, <a href="/search/gr-qc?searchtype=author&query=Zoe%2C+H">Heeseung Zoe</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="1108.5886v3-abstract-short" style="display: inline;"> We examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. Most of the e-foldings are attained around the critical point for each inflationary trajectories. If the coupling constants $g_i$ have the parametric… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1108.5886v3-abstract-full').style.display = 'inline'; document.getElementById('1108.5886v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1108.5886v3-abstract-full" style="display: none;"> We examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. Most of the e-foldings are attained around the critical point for each inflationary trajectories. If the coupling constants $g_i$ have the parametric relations generated as the power of the relative energy scale of inflation $H_0$ to the ultraviolet cutoff $螞$, a successful inflation with more than 60 e-foldings occurs near the critical point. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1108.5886v3-abstract-full').style.display = 'none'; document.getElementById('1108.5886v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 June, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 August, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">14 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int. J. Mod. Phys. D 21, 1250062 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1103.0300">arXiv:1103.0300</a> <span> [<a href="https://arxiv.org/pdf/1103.0300">pdf</a>, <a href="https://arxiv.org/ps/1103.0300">ps</a>, <a href="https://arxiv.org/format/1103.0300">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.83.104040">10.1103/PhysRevD.83.104040 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamics of stringy congruence in early universe </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Cho%2C+Y+S">Yong Seung Cho</a>, <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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="1103.0300v1-abstract-short" style="display: inline;"> We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both tim… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.0300v1-abstract-full').style.display = 'inline'; document.getElementById('1103.0300v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1103.0300v1-abstract-full" style="display: none;"> We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. In this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and the shear in terms of the expansion of the universe. In appendix we investigate the geodesic surface congruence of the null strings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.0300v1-abstract-full').style.display = 'none'; document.getElementById('1103.0300v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 March, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">11 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D83:104040,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1005.4169">arXiv:1005.4169</a> <span> [<a href="https://arxiv.org/pdf/1005.4169">pdf</a>, <a href="https://arxiv.org/ps/1005.4169">ps</a>, <a href="https://arxiv.org/format/1005.4169">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"> Hydrodynamics and global embeddings of Taub-NUT spacetime </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+S">Sung-Won Kim</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="1005.4169v1-abstract-short" style="display: inline;"> On Taub-NUT spacetime, we investigate hydrodynamic properties of perfect fluid spiraling inward toward the spacetime along a conical surface. On the equatorial plane of the Taub-NUT spacetime, we derive radial equations of motion with effective potentials and the Euler equation for steady state axisymmetric fluid. Higher dimensional global embeddings are constructed inside and outside the event ho… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.4169v1-abstract-full').style.display = 'inline'; document.getElementById('1005.4169v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1005.4169v1-abstract-full" style="display: none;"> On Taub-NUT spacetime, we investigate hydrodynamic properties of perfect fluid spiraling inward toward the spacetime along a conical surface. On the equatorial plane of the Taub-NUT spacetime, we derive radial equations of motion with effective potentials and the Euler equation for steady state axisymmetric fluid. Higher dimensional global embeddings are constructed inside and outside the event horizons of the Taub-NUT spacetime. We also study the effective potentials of particles on the Taub-NUT spacetime in terms of gravitational magnetic monopole strength of the source, total energy and angular momentum per unit rest mass of the particle. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.4169v1-abstract-full').style.display = 'none'; document.getElementById('1005.4169v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.2370">arXiv:0903.2370</a> <span> [<a href="https://arxiv.org/pdf/0903.2370">pdf</a>, <a href="https://arxiv.org/ps/0903.2370">ps</a>, <a href="https://arxiv.org/format/0903.2370">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S2010194511000468">10.1142/S2010194511000468 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Critical Reviews of Causal Patch Measure over the Multiverse </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S+E">Sungwook E. Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Yeom%2C+D">Dong-han Yeom</a>, <a href="/search/gr-qc?searchtype=author&query=Zoe%2C+H">Heeseung Zoe</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0903.2370v2-abstract-short" style="display: inline;"> In this talk, the causal patch measure based on black hole complementarity is critically reviewed. By noticing the similarities between the causal structure of an inflationary dS space and that of a black hole, we have considered the complementarity principle between the inside and the outside of the causal horizon as an attractive way to count the inflationary multiverse. Even though the causal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.2370v2-abstract-full').style.display = 'inline'; document.getElementById('0903.2370v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.2370v2-abstract-full" style="display: none;"> In this talk, the causal patch measure based on black hole complementarity is critically reviewed. By noticing the similarities between the causal structure of an inflationary dS space and that of a black hole, we have considered the complementarity principle between the inside and the outside of the causal horizon as an attractive way to count the inflationary multiverse. Even though the causal patch measure relieves the Boltzmann brain problem and stresses physical reality based on observations, it could be challenged by the construction of counterexamples, both on regular black holes and charged black holes, to black hole complementarity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.2370v2-abstract-full').style.display = 'none'; document.getElementById('0903.2370v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 December, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures; A proceeding for CosPA2008. Talk on the 29th of October, 2008, Pohang, Korea</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Int.J.Mod.Phys.Conf.Ser.1:317-322, 2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0809.1480">arXiv:0809.1480</a> <span> [<a href="https://arxiv.org/pdf/0809.1480">pdf</a>, <a href="https://arxiv.org/ps/0809.1480">ps</a>, <a href="https://arxiv.org/format/0809.1480">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/10.1088/1126-6708/2008/12/080">10.1088/1126-6708/2008/12/080 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Black hole complementarity with local horizons and Horowitz-Maldacena's proposal </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S+E">Sungwook E. Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Hwang%2C+D">Dong-il Hwang</a>, <a href="/search/gr-qc?searchtype=author&query=Yeom%2C+D">Dong-han Yeom</a>, <a href="/search/gr-qc?searchtype=author&query=Zoe%2C+H">Heeseung Zoe</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0809.1480v3-abstract-short" style="display: inline;"> To implement the consistent black hole complementarity principle, we need two assumptions: first, there exists a singularity near the center, and second, global horizons are the same as local horizons. However, these assumptions are not true in general. In this paper, the authors study a charged black hole in which the second assumption may not hold. From the previous simulations, we have argued… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.1480v3-abstract-full').style.display = 'inline'; document.getElementById('0809.1480v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0809.1480v3-abstract-full" style="display: none;"> To implement the consistent black hole complementarity principle, we need two assumptions: first, there exists a singularity near the center, and second, global horizons are the same as local horizons. However, these assumptions are not true in general. In this paper, the authors study a charged black hole in which the second assumption may not hold. From the previous simulations, we have argued that the event horizon is quite close to the outer horizon, and it seems not harmful to black hole complementarity; however, the Cauchy horizon can be different from the inner horizon, and a violation of complementarity will be possible. To maintain complementarity, we need to assume a selection principle between the singularity and the Hawking radiation generating surface; we suggest that Horowitz-Maldacena's proposal can be useful for this purpose. Finally, we discussed some conditions under which the selection principle may not work. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.1480v3-abstract-full').style.display = 'none'; document.getElementById('0809.1480v3-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 December, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 11 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> JHEP 0812:080,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0808.1709">arXiv:0808.1709</a> <span> [<a href="https://arxiv.org/pdf/0808.1709">pdf</a>, <a href="https://arxiv.org/ps/0808.1709">ps</a>, <a href="https://arxiv.org/format/0808.1709">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/10.1088/0264-9381/27/4/045014">10.1088/0264-9381/27/4/045014 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The causal structure of dynamical charged black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S+E">Sungwook E. Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Hwang%2C+D">Dong-il Hwang</a>, <a href="/search/gr-qc?searchtype=author&query=Stewart%2C+E+D">Ewan D. Stewart</a>, <a href="/search/gr-qc?searchtype=author&query=Yeom%2C+D">Dong-han Yeom</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="0808.1709v3-abstract-short" style="display: inline;"> We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes space-like and is separated from the Cauchy horizon, which is parallel to t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0808.1709v3-abstract-full').style.display = 'inline'; document.getElementById('0808.1709v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0808.1709v3-abstract-full" style="display: none;"> We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes space-like and is separated from the Cauchy horizon, which is parallel to the out-going null direction. Since a charged black hole must eventually transit to a neutral black hole, we studied the neutralization of the black hole and observed that the inner horizon evolves into a space-like singularity, generating a Cauchy horizon which is parallel to the in-going null direction. Since the mass function is finite around the inner horizon, the inner horizon is regular and penetrable in a general relativistic sense. However, since the curvature functions become trans-Planckian, we cannot saymore about the region beyond the inner horizon, and it is natural to say that there is a 'physical' space-like singularity. However, if we assume an exponentially large number of massless scalar fields, our results can be extended beyond the inner horizon. In this case, strong cosmic censorship and black hole complementarity can be violated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0808.1709v3-abstract-full').style.display = 'none'; document.getElementById('0808.1709v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 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">23 pages, 23 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Class.Quant.Grav.27:045014,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0806.2061">arXiv:0806.2061</a> <span> [<a href="https://arxiv.org/pdf/0806.2061">pdf</a>, <a href="https://arxiv.org/ps/0806.2061">ps</a>, <a href="https://arxiv.org/format/0806.2061">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.067301">10.1103/PhysRevD.78.067301 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Singularities in geodesic surface congruence </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Cho%2C+Y+S">Yong Seung Cho</a>, <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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="0806.2061v1-abstract-short" style="display: inline;"> In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the con… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0806.2061v1-abstract-full').style.display = 'inline'; document.getElementById('0806.2061v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0806.2061v1-abstract-full" style="display: none;"> In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the time-like and null string congruences produce the same inequality equation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0806.2061v1-abstract-full').style.display = 'none'; document.getElementById('0806.2061v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 June, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:067301,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0801.3781">arXiv:0801.3781</a> <span> [<a href="https://arxiv.org/pdf/0801.3781">pdf</a>, <a href="https://arxiv.org/ps/0801.3781">ps</a>, <a href="https://arxiv.org/format/0801.3781">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.047503">10.1103/PhysRevD.78.047503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higher dimensional cosmological model with a phantom field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S+T">S. T. Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Lee%2C+J">J. Lee</a>, <a href="/search/gr-qc?searchtype=author&query=Lee%2C+T+H">T. H. Lee</a>, <a href="/search/gr-qc?searchtype=author&query=OH%2C+P">P. OH</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="0801.3781v3-abstract-short" style="display: inline;"> We consider a higher dimensional gravity theory with a negative kinetic energy scalar field and a cosmological constant. We find that the theory admits an exact cosmological solution for the scale factor of our universe. It has the feature that the universe undergoes a continuous transition from deceleration to acceleration at some finite time. This transition time can be interpreted as that of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0801.3781v3-abstract-full').style.display = 'inline'; document.getElementById('0801.3781v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0801.3781v3-abstract-full" style="display: none;"> We consider a higher dimensional gravity theory with a negative kinetic energy scalar field and a cosmological constant. We find that the theory admits an exact cosmological solution for the scale factor of our universe. It has the feature that the universe undergoes a continuous transition from deceleration to acceleration at some finite time. This transition time can be interpreted as that of recent acceleration of our universe. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0801.3781v3-abstract-full').style.display = 'none'; document.getElementById('0801.3781v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 May, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 January, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, 2 figures; References added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:047503,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/gr-qc/0601023">arXiv:gr-qc/0601023</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0601023">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0601023">ps</a>, <a href="https://arxiv.org/format/gr-qc/0601023">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/10.1393/ncb/i2005-10150-0">10.1393/ncb/i2005-10150-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Warped products and black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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/0601023v1-abstract-short" style="display: inline;"> We apply the warped product spacetime scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordstr枚m-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes. </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0601023v1-abstract-full" style="display: none;"> We apply the warped product spacetime scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordstr枚m-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0601023v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0601023v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">6 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nuovo Cim. B120 (2005) 1227-1234 </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/0509016">arXiv:gr-qc/0509016</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0509016">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0509016">ps</a>, <a href="https://arxiv.org/format/gr-qc/0509016">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2005.07.045">10.1016/j.physletb.2005.07.045 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Thermodynamics of (1+1) dilatonic black holes in global flat embedding scheme </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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/0509016v1-abstract-short" style="display: inline;"> We study thermodynamics of (1+1) dimensional dilatonic black holes in global embedding Minkowski space scheme. Exploiting geometrical entropy correction we construct consistent entropy for the charged dilatonic black hole. Moreover, (1+1) dilatonic black holes with higher order terms are shown to possess (3+2) global flat embedding structures regardless of the details of the lapse function, and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0509016v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0509016v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0509016v1-abstract-full" style="display: none;"> We study thermodynamics of (1+1) dimensional dilatonic black holes in global embedding Minkowski space scheme. Exploiting geometrical entropy correction we construct consistent entropy for the charged dilatonic black hole. Moreover, (1+1) dilatonic black holes with higher order terms are shown to possess (3+2) global flat embedding structures regardless of the details of the lapse function, and to yield a generic entropy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0509016v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0509016v1-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 September, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">5 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett. B623 (2005) 135-140 </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/0503079">arXiv:gr-qc/0503079</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0503079">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0503079">ps</a>, <a href="https://arxiv.org/format/gr-qc/0503079">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"> Hydrodynamics and global structure of rotating Schwarzschild black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+S">Sung-Won Kim</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/0503079v1-abstract-short" style="display: inline;"> Exploiting a rotating Schwarzschild black hole metric, we study hydrodynamic properties of perfect fluid whirling inward toward the black holes along a conical surface. On the equatorial plane of the rotating Schwarzschild black hole, we derive radial equations of motion with effective potentials and the Euler equation for steady state axisymmetric fuid. Moreover, numerical analysis is performed… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0503079v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0503079v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0503079v1-abstract-full" style="display: none;"> Exploiting a rotating Schwarzschild black hole metric, we study hydrodynamic properties of perfect fluid whirling inward toward the black holes along a conical surface. On the equatorial plane of the rotating Schwarzschild black hole, we derive radial equations of motion with effective potentials and the Euler equation for steady state axisymmetric fuid. Moreover, numerical analysis is performed to figure out effective potentials of particles on the rotating Schwarzschild manifolds in terms of angular velocity, total energy and angular momentum per unit rest mass. Higher dimensional global embeddings are also constructed inside and outside the event horizons of the rotating Schwarzschild black holes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0503079v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0503079v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 March, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">6 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Korean Phys.Soc. 49 (2006) S748-S754 </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/0410090">arXiv:gr-qc/0410090</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0410090">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0410090">ps</a>, <a href="https://arxiv.org/format/gr-qc/0410090">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"> Warped products and FRW cosmology </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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/0410090v1-abstract-short" style="display: inline;"> We study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe, by exploiting Lorentzian warped product scheme. Introducing double discontinuities occurred at the radiation-matter and matter-lambda phase transitions, we also discuss non-smooth features of the spatially flat Friedma… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0410090v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0410090v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0410090v1-abstract-full" style="display: none;"> We study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe, by exploiting Lorentzian warped product scheme. Introducing double discontinuities occurred at the radiation-matter and matter-lambda phase transitions, we also discuss non-smooth features of the spatially flat Friedmann-Robertson-Walker universe. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0410090v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0410090v1-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 October, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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">4 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Korean Phys.Soc. 45 (2004) S95-S98 </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/0310118">arXiv:gr-qc/0310118</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0310118">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0310118">ps</a>, <a href="https://arxiv.org/format/gr-qc/0310118">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/10.1023/B:GERG.0000035958.55759.24">10.1023/B:GERG.0000035958.55759.24 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Complete higher dimensional global embedding structures of various black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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/0310118v2-abstract-short" style="display: inline;"> We study global flat embeddings inside and outside of event horizons of black holes such as Schwarzschild and Reissner-Nordstr枚m black holes, and of de Sitter space. On these overall patches of the curved manifolds we investigate four accelerations and Hawking temperatures by introducing relevant Killing vectors. </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0310118v2-abstract-full" style="display: none;"> We study global flat embeddings inside and outside of event horizons of black holes such as Schwarzschild and Reissner-Nordstr枚m black holes, and of de Sitter space. On these overall patches of the curved manifolds we investigate four accelerations and Hawking temperatures by introducing relevant Killing vectors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310118v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0310118v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 January, 2004; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 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">8 pages, revised with references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Gen.Rel.Grav. 36 (2004) 1919-1929 </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/0310046">arXiv:gr-qc/0310046</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0310046">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0310046">ps</a>, <a href="https://arxiv.org/format/gr-qc/0310046">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2003.10.050">10.1016/j.physletb.2003.10.050 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> SO(3,2)/Sp(2) symmetries in BTZ black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</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/0310046v1-abstract-short" style="display: inline;"> We study global flat embeddings, three accelerations and Hawking temperatures of the BTZ black holes in the framework of two-time physics scheme associated with Sp(2) local symmetry, to construct their corresponding SO(3,2) global symmetry invariant Lagrangians both inside and outside event horizons. Moreover, the Sp(2) local symmetry is discussed in terms of the metric time-independence. </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0310046v1-abstract-full" style="display: none;"> We study global flat embeddings, three accelerations and Hawking temperatures of the BTZ black holes in the framework of two-time physics scheme associated with Sp(2) local symmetry, to construct their corresponding SO(3,2) global symmetry invariant Lagrangians both inside and outside event horizons. Moreover, the Sp(2) local symmetry is discussed in terms of the metric time-independence. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0310046v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0310046v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 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">9 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett. B578 (2004) 187-194; Erratum-ibid. B638 (2006) 552-553 </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/0303059">arXiv:gr-qc/0303059</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0303059">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0303059">ps</a>, <a href="https://arxiv.org/format/gr-qc/0303059">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1142/S0217732306019839">10.1142/S0217732306019839 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Can wormholes have negative temperatures? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+S">Sung-Won Kim</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/0303059v2-abstract-short" style="display: inline;"> We study (3+1) Morris-Thorne wormhole to investigate its higher dimensional embedding structures and thermodynamic properties. It is shown that the wormhole is embedded in (5+2) global embedding Minkowski space. This embedding enables us to construct the wormhole entropy and Hawking temperature by exploiting Unruh effects. We also propose a possibility of negative temperature originated from exo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0303059v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0303059v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0303059v2-abstract-full" style="display: none;"> We study (3+1) Morris-Thorne wormhole to investigate its higher dimensional embedding structures and thermodynamic properties. It is shown that the wormhole is embedded in (5+2) global embedding Minkowski space. This embedding enables us to construct the wormhole entropy and Hawking temperature by exploiting Unruh effects. We also propose a possibility of negative temperature originated from exotic matter distribution of the wormhole. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0303059v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0303059v2-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 July, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 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">5 pages, typos corrected, 1 reference added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Mod.Phys.Lett. A21 (2006) 789-794 </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/0209058">arXiv:gr-qc/0209058</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0209058">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0209058">ps</a>, <a href="https://arxiv.org/format/gr-qc/0209058">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"> (2+1) dimensional black holes in warped product scheme </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Choi%2C+J">Jaedong Choi</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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/0209058v1-abstract-short" style="display: inline;"> Exploiting a multiply warped product manifold scheme, we study the interior solutions of the Banados-Teitelboim-Zanelli black holes and the exterior solutions of the de Sitter black holes in the (2+1) dimensions. </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0209058v1-abstract-full" style="display: none;"> Exploiting a multiply warped product manifold scheme, we study the interior solutions of the Banados-Teitelboim-Zanelli black holes and the exterior solutions of the de Sitter black holes in the (2+1) dimensions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0209058v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0209058v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 September, 2002; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2002. </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</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> SOGANG-HEP 300/02 </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/0110057">arXiv:gr-qc/0110057</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0110057">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0110057">ps</a>, <a href="https://arxiv.org/format/gr-qc/0110057">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="General Relativity and Quantum Cosmology">gr-qc</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Global Embeddings of Two-dimensional Dilatonic Black Holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+W+T">Won Tae Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Oh%2C+J+J">John J. Oh</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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/0110057v2-abstract-short" style="display: inline;"> We obtain minimal (2+1) and (2+2) dimensional global flat embeddings of uncharged and charged dilatonic black holes in (1+1) dimensions, respectively. Moreover, we obtain the Hawking temperatures and the black hole ones of these dilatonic black holes. However, even though the minimal flat embedding structures are mathematically meaningful, through this minimal embeddings the proper entropies are… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0110057v2-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0110057v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0110057v2-abstract-full" style="display: none;"> We obtain minimal (2+1) and (2+2) dimensional global flat embeddings of uncharged and charged dilatonic black holes in (1+1) dimensions, respectively. Moreover, we obtain the Hawking temperatures and the black hole ones of these dilatonic black holes. However, even though the minimal flat embedding structures are mathematically meaningful, through this minimal embeddings the proper entropies are shown to be unattainable, contrast to the cases of other black holes in (2+1) or much higher dimensions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0110057v2-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0110057v2-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 February, 2003; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 October, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2001. </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, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> SOGANG-HEP 285/01 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Korean Phys.Soc.42:23-28,2003 </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/0006025">arXiv:gr-qc/0006025</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0006025">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0006025">ps</a>, <a href="https://arxiv.org/format/gr-qc/0006025">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.62.064021">10.1103/PhysRevD.62.064021 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Global embeddings of scalar-tensor theories in (2+1)-dimensions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+W+T">Won Tae Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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/0006025v1-abstract-short" style="display: inline;"> We obtain (3+3)- or (3+2)-dimensional global flat embeddings of four uncharged and charged scalar-tensor theories with the parameters B or L in the (2+1)-dimensions, which are the non-trivially modified versions of the Banados-Teitelboim-Zanelli (BTZ) black holes. The limiting cases B=0 or L=0 exactly are reduced to the Global Embedding Minkowski Space (GEMS) solution of the BTZ black holes. </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0006025v1-abstract-full" style="display: none;"> We obtain (3+3)- or (3+2)-dimensional global flat embeddings of four uncharged and charged scalar-tensor theories with the parameters B or L in the (2+1)-dimensions, which are the non-trivially modified versions of the Banados-Teitelboim-Zanelli (BTZ) black holes. The limiting cases B=0 or L=0 exactly are reduced to the Global Embedding Minkowski Space (GEMS) solution of the BTZ black holes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0006025v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0006025v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 June, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> SOGANG-HEP 270/00 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D62 (2000) 064021 </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/0003097">arXiv:gr-qc/0003097</a> <span> [<a href="https://arxiv.org/pdf/gr-qc/0003097">pdf</a>, <a href="https://arxiv.org/ps/gr-qc/0003097">ps</a>, <a href="https://arxiv.org/format/gr-qc/0003097">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.62.024024">10.1103/PhysRevD.62.024024 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Higher dimensional flat embeddings of (2+1) dimensional black holes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/gr-qc?searchtype=author&query=Hong%2C+S">Soon-Tae Hong</a>, <a href="/search/gr-qc?searchtype=author&query=Kim%2C+Y">Yong-Wan Kim</a>, <a href="/search/gr-qc?searchtype=author&query=Park%2C+Y">Young-Jai Park</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/0003097v1-abstract-short" style="display: inline;"> We obtain the higher dimensional global flat embeddings of static, rotating, and charged BTZ black holes. On the other hand, we also study the similar higher dimensional flat embeddings of the (2+1) de Sitter black holes which are the counterparts of the anti-de Sitter BTZ black holes. As a result, the charged dS black hole is shown to be embedded in (3+2) GEMS, contrast to the charged BTZ one h… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0003097v1-abstract-full').style.display = 'inline'; document.getElementById('gr-qc/0003097v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="gr-qc/0003097v1-abstract-full" style="display: none;"> We obtain the higher dimensional global flat embeddings of static, rotating, and charged BTZ black holes. On the other hand, we also study the similar higher dimensional flat embeddings of the (2+1) de Sitter black holes which are the counterparts of the anti-de Sitter BTZ black holes. As a result, the charged dS black hole is shown to be embedded in (3+2) GEMS, contrast to the charged BTZ one having (3+3) GEMS structure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('gr-qc/0003097v1-abstract-full').style.display = 'none'; document.getElementById('gr-qc/0003097v1-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 March, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2000. </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">16pages, revtex, no 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">Report number:</span> SOGANG-HEP 268/00 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D62 (2000) 024024 </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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