General Relativity and Quantum Cosmology · arXiv:1403.1507 v3 · submitted 6 Mar 2014
Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions
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“It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole.”
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Abstract
Conditions for thermodynamic stability of asymptotically anti-de Sitter rotating black holes in D-dimensions are determined. Local thermodynamic stability requires not only positivity conditions on the specific heat and the moment of inertia tensor but it is also necessary that the adiabatic compressibility be positive. It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole. Thermodynamic stability properties of anti-de Sitter Myers-Perry black holes are investigated for both singly spinning and multi-spinning black holes. Simple expressions are obtained for the specific heat and moment of inertia tensor in any dimension. An analytic expression is obtained for the boundary of the region of parameter space in which such space-times are thermodynamically stable.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.29 · compares with prior results 0.20 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v3). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Conditions for thermodynamic stability of asymptotically anti-de Sitter rotating black holes in D-dimensions are determined. | contribution 0.86 | 0.91 | 0.28 | asserted 0.99 |
| Local thermodynamic stability requires not only positivity conditions on the specific heat and the moment of inertia tensor but it is also necessary that the adiabatic compressibility be positive. | result 0.89 | 0.54 | 0.24 | asserted 1.00 |
| It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole. | result 0.95 | 0.71 | 0.27 | asserted 1.00 |
| Thermodynamic stability properties of anti-de Sitter Myers-Perry black holes are investigated for both singly spinning and multi-spinning black holes. | contribution 0.99 | 0.90 | 0.06 | asserted 0.91 |
| Simple expressions are obtained for the specific heat and moment of inertia tensor in any dimension. | result 0.87 | 0.95 | 0.05 | asserted 1.00 |
| An analytic expression is obtained for the boundary of the region of parameter space in which such space-times are thermodynamically stable. | result 0.96 | 0.95 | 0.30 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v3
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- full text
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- references and citing sentences
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- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,912 input tokens, $0.0002 reported.
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Cited by 2 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Black hole chemistry: thermodynamics with Lambda hep-th · Aug 2016
- Black holes and Boyle's law -- the thermodynamics of the cosmological constant gr-qc · Aug 2014
How the literature uses it
13 arXiv papers cite this in 27 sentences
Papers citing it · 17 sentences without a confident label
Uses its method or tool 1 paper
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To find the isothermal moment of inertia tensor (see also [ref] ), we fix $g$ and substitute $q=q(Q, a, b, r_+, g)$ into the angular momenta (equation [ref]) the angular velocities (equation [ref]) and the temperature (equation [ref]).
Thermodynamics of a rotating black hole in minimal five-dimensional gauged supergravity · Thermodynamic stability · 0.93
Compares with it 1 paper
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Similar instabilities have been observed for charged AdS black holes [ref] and rotating AdS black holes with constant angular momentum [ref] .
Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality · The critical behavior of the boundary conformal field theory · 0.98
Cites it as support 2 papers
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However, if $P=0$, it always has a negative eigenvalue, [ref] , and there are no thermodynamically stable asymptotically flat black holes in any dimension, regardless of rotation or charge.
The intrinsic curvature of thermodynamic potentials for black holes with critical points · Thermodynamic metrics · 0.97
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The basic results—Van der Waals behavior, reentrant phase transitions, triple points, and Carnot-type cycles—are extremely robust, having been replicated in a broad variety of settings and contexts [ref] .
Black hole chemistry: thermodynamics with Lambda · Future of black hole chemistry · 0.97
Cites it as background 6 papers
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In this section we analyse the rich and complicated thermodynamic behaviour of the rotating hairy black hole solutions in the microcanonical, canonical and grand-canonical ensembles [ref] .
Rotating Hairy Black Holes in AdS$_5\times$S$^5$ · Thermodynamics · 0.84
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In recent years, considerable attentions have been arisen to investigate thermodynamic phase transition of anti-de Sitter (AdS) black holes in an extended phase space, where the first law of black hole thermodynamics is extended by treating the cosmological constant as a thermodynamic variable [ref] .
Thermodynamic geometry and phase transition of spinning AdS black holes · Introduction · 0.94
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One of them, the black hole adiabatic compressibility [ref] has attracted attention in connection with black hole stability [ref] (see also [ref] ).
Black hole chemistry: thermodynamics with Lambda · Black hole compressibility · 0.86
What it cites · 24 sentences without a confident label
Builds on 3 papers
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This was proven in [ref] for $P=0$ and the same analysis goes through for any $P≥0$.
On the thermodynamic stability of rotating black holes in higher dimensions -- a comparison of thermodynamic ensembles · General stability criteria · 0.80
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This extends the asymptotically flat result in [ref] to $λ0$.
The compressibility of rotating black holes in D-dimensions · Isentropic moment of inertia · 1.00
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This generalises the asymptotically anti-de Sitter $D=4$ case derived in [ref] to arbitrary $D$.
Semiclassical instabilities of Kerr-AdS black holes · Specific heat at constant angular velocity · 0.99
Uses the method or tool of 1 paper
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The specific heat at constant $Ω$ is straightforward to determine, using the same kind if calculations as those in [ref]
On the thermodynamic stability of rotating black holes in higher dimensions -- a comparison of thermodynamic ensembles · Specific heat at constant angular velocity · 0.99
Compares with 3 papers
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In asymptotically flat Myers-Perry space times this reduces to the result [equation] in [ref] .
On the thermodynamic stability of rotating black holes in higher dimensions -- a comparison of thermodynamic ensembles · Specific Heat · 0.81
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For singly spinning black holes, $n=1$, thermodynamic stability was examined in [ref] and the upper left figure is essentially the same as figure 2 in that reference, expressed in slightly different variables.
Ultraspinning instability of anti-de Sitter black holes · Specific Heat · 1.00
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With the substitution $λ→- g^2$ ([ref]) also agrees with the black hole thermodynamic volume quoted in [ref] for $Λ> 0$, again determined by assuming the Smarr relation holds.
Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes · Thermodynamic volume · 0.87
Cites as background 6 papers
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The literature here is not as comprehensive as for the asymptotically de Sitter case, though there has been significant progress in specific cases [ref] - [ref] .
Enthalpy and the Mechanics of AdS Black Holes · Introduction · 0.96
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The literature here is not as comprehensive as for the asymptotically de Sitter case, though there has been significant progress in specific cases [ref] - [ref] .
Semiclassical instabilities of Kerr-AdS black holes · Introduction · 0.96
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These thermodynamic constraints must of course be supplemented by possible further constraints required to avoid the super-radiant instability of the classical solutions themselves, discussed in [ref] and [ref] - [ref] .
Small Kerr-anti-de Sitter black holes are unstable · Conclusions · 0.87
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