Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Sheykin, A. A.; Solovyev, Dmitry; Paston, S. A.

doi:10.3390/sym11070841

Cited by 8 publications

(9 citation statements)

References 34 publications

(65 reference statements)

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“…As in the case of the BTZ black hole, one may construct thermodynamic-like quantities for the accelerating observers that satisfy the laws of thermodynamics. Although reasonable in this context, there is no independent check -as far as I am aware -in the literature on the validity of the expression for the entropy, equation (33). Possible work terms are discussed in appendix C.…”

Section: Schwarzschild Spacetimesmentioning

confidence: 99%

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On energy for accelerating observers in black hole spacetimes

Major

2022

Preprint

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Quasi-local energies for constantly accelerating observers in Bañados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.Date: February 2022. 1 I assume that these observers are not unlike us. In addition to the usual garden variety meter sticks and clocks, I assume that they have access more sophisticated equipment e.g. accelerometers, radar or laser ranging, bolometers, and telescopes.

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Section: Schwarzschild Spacetimesmentioning

confidence: 99%

“…4 Since Newton's constant, the speed of light, and mass do not create a length in (2 + 1)-dimensional gravity, the model must have an additional scale [33].…”

Section: Btz Spacetimesmentioning

confidence: 99%

On energy for accelerating observers in black hole spacetimes

Major

2022

Preprint

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“…We emphasize that the JCF theorem consider only local embeddings, and when passing to global embeddings, the required dimension of the ambient space increases sharply [3]. However, in specific cases, even for global embeddings, the class of the embedding can be smaller, see, for example, [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…The only global embedding [7] turns out to be closely related to the maximum analytic extension of the Schwarzschild metric by the Kruskal-Shekeres coordinates (see the note at the end of [7]). In general, a lot of works have been devoted to the construction of explicit embeddings of various black holes, including charged and rotating ones; see, for example, the links in [5]. Other physically interesting metrics include various cosmological models, e.g., Friedmann-Robertson-Walker metric that describe the expanding universe.…”

Section: Introductionmentioning

confidence: 99%

Nontrivial Isometric Embeddings for Flat Spaces

Paston

Zaitseva

2021

Universe

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Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

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“…Deser and Levin [6][7][8] showed that the Hawking temperature for a fiducial observer in a curved spacetime can be considered as the Unruh one for a uniformly accelerated observer in a higher-dimensional flat spacetime. Since then, there have been a lot of works on the GEMS approach to confirm these ideas in various other spacetimes [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and an interesting extension to embedding gravity [25][26][27][28]. Later, Brynjolfsson and Thorlacius (BT) [29] introduced a local temperature measured by a freely falling observer in the GEMS method.…”

Section: Introductionmentioning

confidence: 99%

GEMS Embeddings of Schwarzschild and RN Black Holes in Painlevé-Gullstrand Spacetimes

2021

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Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3 + 1)-dimensional Schwarzschild and Reissner-Nordström (RN) black holes written by the Painlevé-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.

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Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Cited by 8 publications

References 34 publications

On energy for accelerating observers in black hole spacetimes

On energy for accelerating observers in black hole spacetimes

Nontrivial Isometric Embeddings for Flat Spaces

GEMS Embeddings of Schwarzschild and RN Black Holes in Painlevé-Gullstrand Spacetimes

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