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Thermodynamics and Stability of Higher Dimensional Rotating (Kerr) AdS Black Holes
General Relativity and Quantum Cosmology · Submitted 21 Jun 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius.
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The abstract, sentence by sentence
We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six dimensional case is marginal.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. | contribution 0.95 | 0.90 | 0.06 | asserted 0.56 |
| s1 | We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. | result 1.00 | 0.95 | 0.52 | asserted 1.00 |
| s2 | In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. | result 0.91 | 0.82 | 0.16 | asserted 0.98 |
| s3 | We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. | result 1.00 | 0.96 | 0.15 | asserted 1.00 |
| s4 | The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. | result 1.00 | 0.70 | 0.08 | asserted 1.00 |
| s5 | We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). | result 1.00 | 0.91 | 0.12 | asserted 1.00 |
| s6 | In this last context, the six dimensional case is marginal. | result 0.67 | 0.63 | 0.04 | asserted 0.97 |
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Original abstract
We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six dimensional case is marginal.
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How the literature uses it
9 arXiv papers cite this in 10 sentences
Papers citing it · 6 sentences without a confident label
Cites it as background 4 papers
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The thermodynamics of MPAdS was carefully discussed in [ref] (see also [ref] ), and phase transitions for the rotating black hole solutions were studied in [ref] .
Black resonators and geons in AdS$_5$ · Introduction · 0.99
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While some of our findings may have already been presented in existing literature, they have been scattered across various texts[See for example [ref] .].
On Thermodynamic Stability of Black Holes. Part II: AdS Family of Solutions · Conclusion · 0.82
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It is worth mentioning that related meaningful investigations on thermodynamical stability of AdS black holes can be seen in Refs. [ref] .
Thermodynamical stability of $f(R)$-AdS black holes in grand canonical ensemble · Introduction · 0.91
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