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Thermodynamics of four-dimensional black objects in the warped compactification
General Relativity and Quantum Cosmology · Submitted 26 Jun 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case.
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The abstract, sentence by sentence
We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized black hole on a flat brane is negative, and it differs from the one previously derived. We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case. We also find a braneworld analogue of the Hawking-Page transition between the BTZ black string and thermal AdS branes. The localized black holes on a de Sitter brane is discussed by considering Nariai instanton, comparing the study of "black cigar" in the five-dimensional braneworld model.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. | contribution 0.62 | 0.68 | 0.05 | asserted 0.95 |
| s1 | After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. | method 0.60 | 0.97 | 0.16 | asserted 1.00 |
| s2 | We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. | result 1.00 | 0.90 | 0.16 | asserted 1.00 |
| s3 | The thermodynamic mass of the localized black hole on a flat brane is negative, and it differs from the one previously derived. | result 1.00 | 0.93 | 0.19 | asserted 1.00 |
| s4 | We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case. | result 0.99 | 0.95 | 0.17 | asserted 1.00 |
| s5 | We also find a braneworld analogue of the Hawking-Page transition between the BTZ black string and thermal AdS branes. | result 0.99 | 0.94 | 0.18 | asserted 1.00 |
| s6 | The localized black holes on a de Sitter brane is discussed by considering Nariai instanton, comparing the study of "black cigar" in the five-dimensional braneworld model. | contribution 0.92 | 0.80 | 0.07 | asserted 0.94 |
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The paper
Original abstract
We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized black hole on a flat brane is negative, and it differs from the one previously derived. We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case. We also find a braneworld analogue of the Hawking-Page transition between the BTZ black string and thermal AdS branes. The localized black holes on a de Sitter brane is discussed by considering Nariai instanton, comparing the study of "black cigar" in the five-dimensional braneworld model.
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References
How the literature uses it
14 arXiv papers cite this in 28 sentences
Papers citing it · 14 sentences without a confident label
Builds on it 1 paper
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The case where $α=0$ has been worked out as a special case and discussed [ref] , but for general $α$ new features arise in $C_p(T)$. $C_p$ in this case is given by
Specific Heats for Rotating Quantum BTZ Black Holes in Extended Thermodynamics · $C_p$ at fixed $α$ · 0.83
Uses its method or tool 5 papers
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We have [ref] [equation] where [equation] is the brane stress tensor and $[F(z)]$ measures the discontinuity [equation] of $F$ at $z$ [ref] .
Charged rotating quantum black holes · Solution and braneworld embedding · 0.91
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Each quantity may be derived by identifying the bulk on-shell Euclidean action with the canonical free energy [ref] .
Quantum inequalities for quantum black holes · Introduction · 0.84
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Such an approach was taken in [ref] (see Appendix [ref] for details).
Three-dimensional quantum black holes: a primer · Gravitational path integral approach · 0.81
Uses its data or values 1 paper
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The mass $M$, temperature $T$ and entropy $S$ of the classical bulk black hole are [ref] (see also [ref] ) M = √(1+ν^2)/2G_3z^2(1-νz^3)(1+νz)/(1+3z^2+2νz^3)^2 , T = 1/2πℓ_3z(2+3νz+νz^3)/1+3z^2+2νz^3 , S = πℓ_3√(1+ν^2)/G_3z/1+3z^2+2νz^3 ,
Reentrant phase transitions of quantum black holes · Introduction · 0.88
Compares with it 3 papers
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This yields [equation] consistent with [ref] .
Criticality and thermodynamic geometry of quantum BTZ black holes · Thermodynamics of the quantum BTZ black hole · 0.83
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Collecting all terms, the renormalized on-shell action is [equation] This result agrees with the much earlier computation of the action by Kudoh and Kurita for a two-brane configuration [ref] ; see also [ref] .
Quantum Solitons · Total action · 1.00
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Precisely, let $z_1$ be the positive root to $4 z^3 ν+ 3 z^2 -1=0$, $z_2$ be the positive root of $νz^3+3z^2-3νz-1=0$, and $z_3=ν^-1/3$ (these coincide with [ref] upon $z→νz$ and $λ=ν^2$).
Reentrant phase transitions of quantum black holes · Introduction · 0.98
Cites it as support 1 paper
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The mass $M$ of the black hole here is related to the conical deficit angle [ref] , as confirmed in [ref] via the Euclidean formulation.
Charged rotating quantum black holes · Solution and braneworld embedding · 0.96
Cites it as background 2 papers
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For details, see Kudoh and Kurita [ref] .].
Thermodynamics of Squashed Kaluza-Klein Black Holes and Black Strings -- A Comparison of Reference Backgrounds -- · The classical action and free energy of the SqKK black hole · 0.82
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These studies have uncovered many fascinating phenomena, such as the quantum Penrose inequality and the quantum reverse isoperimetric inequality [ref] , the construction of doubly holographic thermodynamics [ref] , and various phase transitions [ref] .
Charged rotating quantum black holes · Introduction · 0.97
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