Pub Date : 2021-08-17DOI: 10.1103/PhysRevD.104.084086
A. Azizi, H. Camblong, A. Chakraborty, C. Ordóñez, M. Scully
A quantum-optics approach is used to study the nature of the acceleration radiation due to a random atomic cloud falling freely into a generalized Schwarzschild black hole through a Boulware vacuum. The properties of this horizon brightened acceleration radiation (HBAR) are analyzed with a master equation that is fully developed in a multimode format. A scheme for the coarse-graining average for an atomic cloud is considered, with emphasis on the random injection scenario, which is shown to generate a thermal state. The role played by conformal quantum mechanics (CQM) is shown to be critical for detailed balance via a Boltzmann factor governed by the near-horizon physics, with the unique selection of the Hawking temperature. The HBAR thermal state is the basis for a thermodynamic framework that parallels black hole thermodynamics.
{"title":"Quantum optics meets black hole thermodynamics via conformal quantum mechanics: I. Master equation for acceleration radiation","authors":"A. Azizi, H. Camblong, A. Chakraborty, C. Ordóñez, M. Scully","doi":"10.1103/PhysRevD.104.084086","DOIUrl":"https://doi.org/10.1103/PhysRevD.104.084086","url":null,"abstract":"A quantum-optics approach is used to study the nature of the acceleration radiation due to a random atomic cloud falling freely into a generalized Schwarzschild black hole through a Boulware vacuum. The properties of this horizon brightened acceleration radiation (HBAR) are analyzed with a master equation that is fully developed in a multimode format. A scheme for the coarse-graining average for an atomic cloud is considered, with emphasis on the random injection scenario, which is shown to generate a thermal state. The role played by conformal quantum mechanics (CQM) is shown to be critical for detailed balance via a Boltzmann factor governed by the near-horizon physics, with the unique selection of the Hawking temperature. The HBAR thermal state is the basis for a thermodynamic framework that parallels black hole thermodynamics.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88755164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-27DOI: 10.1103/PhysRevD.104.044063
M. Khuri, G. Weinstein, S. Yamada
We construct a new set of asymptotically flat, static vacuum solutions to the Einstein equations in dimensions 4 and 5, which may be interpreted as a superposition of positive and negative mass black holes. The resulting spacetimes are axisymmetric in 4-dimensions and bi-axisymmetric in 5-dimensions, and are regular away from the negative mass singularities, for instance conical singularities are absent along the axes. In 5-dimensions, the topologies of signed mass black holes used in the construction may be either spheres $S^3$ or rings $S^1 times S^2$; in particular, the negative mass static black ring solution is introduced. A primary observation that facilitates the superposition is the fact that, in Weyl-Papapetrou coordinates, negative mass singularities arise as overlapping singular support for a particular type of Green's function. Furthermore, a careful analysis of conical singularities along axes is performed, and formulas are obtained for their propagation across horizons, negative mass singularities, and corners. The methods are robust, and may be used to construct a multitude of further examples. Lastly, we show that balancing does not occur between any two signed mass black holes of the type studied here in 4 dimensions, while in 5 dimensions two-body balancing is possible.
{"title":"Balancing Static Vacuum Black Holes with Signed Masses in 4 and 5 Dimensions","authors":"M. Khuri, G. Weinstein, S. Yamada","doi":"10.1103/PhysRevD.104.044063","DOIUrl":"https://doi.org/10.1103/PhysRevD.104.044063","url":null,"abstract":"We construct a new set of asymptotically flat, static vacuum solutions to the Einstein equations in dimensions 4 and 5, which may be interpreted as a superposition of positive and negative mass black holes. The resulting spacetimes are axisymmetric in 4-dimensions and bi-axisymmetric in 5-dimensions, and are regular away from the negative mass singularities, for instance conical singularities are absent along the axes. In 5-dimensions, the topologies of signed mass black holes used in the construction may be either spheres $S^3$ or rings $S^1 times S^2$; in particular, the negative mass static black ring solution is introduced. A primary observation that facilitates the superposition is the fact that, in Weyl-Papapetrou coordinates, negative mass singularities arise as overlapping singular support for a particular type of Green's function. Furthermore, a careful analysis of conical singularities along axes is performed, and formulas are obtained for their propagation across horizons, negative mass singularities, and corners. The methods are robust, and may be used to construct a multitude of further examples. Lastly, we show that balancing does not occur between any two signed mass black holes of the type studied here in 4 dimensions, while in 5 dimensions two-body balancing is possible.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72742882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-01DOI: 10.21203/RS.3.RS-229207/V1
A. Bleybel
In this paper we use our results concerning temporal foliations of causal sets in order to provide a new proof of Geroch's Theorem on temporal foliations in a globally hyperbolic spacetime.
{"title":"A new proof of Geroch's theorem on temporal splitting of globally hyperbolic spacetime","authors":"A. Bleybel","doi":"10.21203/RS.3.RS-229207/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-229207/V1","url":null,"abstract":"\u0000 In this paper we use our results concerning temporal foliations of causal sets in order to provide a new proof of Geroch's Theorem on temporal foliations in a globally hyperbolic spacetime.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74583477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-22DOI: 10.1103/PhysRevD.103.126025
M. Bojowald
A new modification of spherically symmetric models inspired by loop quantum gravity has recently been introduced by Benitez, Gambini and Pullin, who claimed that it preserves general covariance. This claim is shown here to be incorrect, based on methods of effective line elements. The same methods imply that the only novel physical effect introduced by the modification is the presence of time-reversal hypersurfaces between classical space-time regions.
{"title":"Noncovariance of “covariant polymerization” in models of loop quantum gravity","authors":"M. Bojowald","doi":"10.1103/PhysRevD.103.126025","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.126025","url":null,"abstract":"A new modification of spherically symmetric models inspired by loop quantum gravity has recently been introduced by Benitez, Gambini and Pullin, who claimed that it preserves general covariance. This claim is shown here to be incorrect, based on methods of effective line elements. The same methods imply that the only novel physical effect introduced by the modification is the presence of time-reversal hypersurfaces between classical space-time regions.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76210921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-16DOI: 10.1103/PhysRevD.103.124052
Shafqat Ul Islam, Sushant G. Ghosh
The recent time witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, suggesting comparing the black hole lensing in general relativity and modified gravity theories. That may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources the surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole, in the strong deflection limits to the hairy Kerr black holes, with deviation parameter $alpha$ and a primary hair $ell_0$. Interestingly, the deflection coefficient $bar{a}$, respectively, increases and decreases with increasing $ell_0$ and $alpha$. $bar{b}$ shows opposite behaviour with $ell_0$ and $alpha$. We also find that the deflection angle $alpha_D$, angular position $theta_{infty}$ and $u_{m}$ decreases, but angular separation $s$ increases with $alpha$. We compare our results with those for Kerr black holes, and also, the formalism is applied to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~mu$as for Sgr A* and $1.96~mu$as for M87*, which are unlikely to get resolved by the current EHT observations.
{"title":"Strong field gravitational lensing by hairy Kerr black holes","authors":"Shafqat Ul Islam, Sushant G. Ghosh","doi":"10.1103/PhysRevD.103.124052","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.124052","url":null,"abstract":"The recent time witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, suggesting comparing the black hole lensing in general relativity and modified gravity theories. That may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources the surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole, in the strong deflection limits to the hairy Kerr black holes, with deviation parameter $alpha$ and a primary hair $ell_0$. Interestingly, the deflection coefficient $bar{a}$, respectively, increases and decreases with increasing $ell_0$ and $alpha$. $bar{b}$ shows opposite behaviour with $ell_0$ and $alpha$. We also find that the deflection angle $alpha_D$, angular position $theta_{infty}$ and $u_{m}$ decreases, but angular separation $s$ increases with $alpha$. We compare our results with those for Kerr black holes, and also, the formalism is applied to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~mu$as for Sgr A* and $1.96~mu$as for M87*, which are unlikely to get resolved by the current EHT observations.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78130378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-14DOI: 10.1103/PHYSREVD.103.084035
K'aroly Csuk'as, I. R'acz
Superradiant scattering of linear spin $s=0,pm 1,pm 2$ fields on Kerr black hole background is investigated in the time domain by integrating numerically the homogeneous Teukolsky master equation. The applied numerical setup has already been used in studying long time evolution and tail behavior of electromagnetic and metric perturbations on rotating black hole background [arXiv:1905.09082v3]. To have a clear setup the initial data is chosen to be of the compact support, while to optimize superradiance the frequency of the initial data is fine tuned. Our most important finding is that the rate of superradiance strongly depends on the relative position of the (compact) support of the initial data and the ergoregion. When they are well-separated then only a modest -- in case of $s=0$ scalar fields negligible -- superradiance occurs, whereas it can get to be amplified significantly whenever the support of the initial data and the ergoregion overlap.
{"title":"Numerical investigation of the dynamics of linear spin \u0000s\u0000 fields on a Kerr background. II. Superradiant scattering","authors":"K'aroly Csuk'as, I. R'acz","doi":"10.1103/PHYSREVD.103.084035","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.084035","url":null,"abstract":"Superradiant scattering of linear spin $s=0,pm 1,pm 2$ fields on Kerr black hole background is investigated in the time domain by integrating numerically the homogeneous Teukolsky master equation. The applied numerical setup has already been used in studying long time evolution and tail behavior of electromagnetic and metric perturbations on rotating black hole background [arXiv:1905.09082v3]. To have a clear setup the initial data is chosen to be of the compact support, while to optimize superradiance the frequency of the initial data is fine tuned. Our most important finding is that the rate of superradiance strongly depends on the relative position of the (compact) support of the initial data and the ergoregion. When they are well-separated then only a modest -- in case of $s=0$ scalar fields negligible -- superradiance occurs, whereas it can get to be amplified significantly whenever the support of the initial data and the ergoregion overlap.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85455455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-13DOI: 10.1103/PHYSREVD.103.084045
Shalabh Gautam, Alex Van'o-Vinuales, D. Hilditch, S. Bose
We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves to mitigate outer boundary effects and, in the future, will help reduce systematic errors in gravitational waveform extraction. We also study a setup with truncation error matching. Our SBP-Stable scheme guarantees energy-balance for a class of linear wave equations at the semidiscrete level. We develop also specialized dissipation operators. The whole construction is made at second order accuracy in spherical symmetry, but could be straightforwardly generalized to higher order or spectral accuracy without symmetry. In a practical implementation we evolve first a scalar field obeying the linear wave equation and observe, as expected, long term stability and norm convergence. We obtain similar results with a potential term. To examine the limitations of the approach we consider a massive field, whose equations of motion do not regularize, and whose dynamics near null infinity, which involve excited incoming pulses that can not be resolved by the code, is very different to that in the massless setting. We still observe excellent energy conservation, but convergence is not satisfactory. Overall our results suggest that compactified hyperboloidal slices are likely to be provably effective whenever the asymptotic solution space is close to that of the wave equation.
{"title":"Summation by parts and truncation error matching on hyperboloidal slices","authors":"Shalabh Gautam, Alex Van'o-Vinuales, D. Hilditch, S. Bose","doi":"10.1103/PHYSREVD.103.084045","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.084045","url":null,"abstract":"We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves to mitigate outer boundary effects and, in the future, will help reduce systematic errors in gravitational waveform extraction. We also study a setup with truncation error matching. Our SBP-Stable scheme guarantees energy-balance for a class of linear wave equations at the semidiscrete level. We develop also specialized dissipation operators. The whole construction is made at second order accuracy in spherical symmetry, but could be straightforwardly generalized to higher order or spectral accuracy without symmetry. In a practical implementation we evolve first a scalar field obeying the linear wave equation and observe, as expected, long term stability and norm convergence. We obtain similar results with a potential term. To examine the limitations of the approach we consider a massive field, whose equations of motion do not regularize, and whose dynamics near null infinity, which involve excited incoming pulses that can not be resolved by the code, is very different to that in the massless setting. We still observe excellent energy conservation, but convergence is not satisfactory. Overall our results suggest that compactified hyperboloidal slices are likely to be provably effective whenever the asymptotic solution space is close to that of the wave equation.","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77459509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.1007/978-0-387-09534-9_15
R. Adler
{"title":"Curved Space and Gravity","authors":"R. Adler","doi":"10.1007/978-0-387-09534-9_15","DOIUrl":"https://doi.org/10.1007/978-0-387-09534-9_15","url":null,"abstract":"","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86285251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.1007/978-3-030-61574-1_2
R. Adler
{"title":"Lorentz Transformations","authors":"R. Adler","doi":"10.1007/978-3-030-61574-1_2","DOIUrl":"https://doi.org/10.1007/978-3-030-61574-1_2","url":null,"abstract":"","PeriodicalId":8455,"journal":{"name":"arXiv: General Relativity and Quantum Cosmology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82233473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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