On Holographic description of the Kerr-Newman-AdS-dS black holes

Bin Chen; Jiang Long

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On Holographic description of the Kerr-Newman-AdS-dS black holes

Bin Chen, Jiang Long

High Energy Physics - Theory · Submitted 1 Jun 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Similar to the Kerr case, this suggests that the Kerr-Newman-AdS-dS black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=\frac{6a(r_++r_\ast)}{k}$ and temperatures $T_L=\frac{k(r_+^2+r_\ast^2+2a^2)}{4\pi a\Xi(r_++r_\ast)}, T_R=\frac{k(r_+-r_\ast)}{4\pi a\Xi}$.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.87 · compares with prior results 0.64 · mentions code or data availability 0.02.

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In this paper, we study the holographic description of the generic four-dimensional non-extremal Kerr-Newman-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, there exists hidden conformal symmetry on the solution space. Similar to the Kerr case, this suggests that the Kerr-Newman-AdS-dS black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=\frac{6a(r_++r_\ast)}{k}$ and temperatures $T_L=\frac{k(r_+^2+r_\ast^2+2a^2)}{4\pi a\Xi(r_++r_\ast)}, T_R=\frac{k(r_+-r_\ast)}{4\pi a\Xi}$. The macroscopic Bekenstein-Hawking entropy could be recovered from the microscopic counting in dual CFT via the Cardy formula. Using the Minkowski prescription, we compute the real-time correlators of the scalar, photon and graviton in near horizon geometry of near extremal Kerr-AdS-dS black hole. In all these cases, the retarded Green's function and the corresponding absorption cross section are in perfect match with CFT prediction. We further discuss the low-frequency scattering of a charged scalar by a Kerr-Newman-AdS-dS black hole and find the dual CFT description.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we study the holographic description of the generic four-dimensional non-extremal Kerr-Newman-AdS-dS black holes.	contribution 0.93	0.82	0.04	asserted 0.70
s1	We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, there exists hidden conformal symmetry on the solution space.	result 1.00	0.95	0.24	asserted 1.00
s2	Similar to the Kerr case, this suggests that the Kerr-Newman-AdS-dS black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=\frac{6a(r_++r_\ast)}{k}$ and temperatures $T_L=\frac{k(r_+^2+r_\ast^2+2a^2)}{4\pi a\Xi(r_++r_\ast)}, T_R=\frac{k(r_+-r_\ast)}{4\pi a\Xi}$.	interpretation 0.57	0.87	0.46	hedged possibility 0.97
s3	The macroscopic Bekenstein-Hawking entropy could be recovered from the microscopic counting in dual CFT via the Cardy formula.	result 0.89	0.71	0.23	hedged possibility 0.98
s4	Using the Minkowski prescription, we compute the real-time correlators of the scalar, photon and graviton in near horizon geometry of near extremal Kerr-AdS-dS black hole.	method 0.68	0.95	0.06	asserted 1.00
s5	In all these cases, the retarded Green's function and the corresponding absorption cross section are in perfect match with CFT prediction.	result 1.00	0.90	0.18	asserted 1.00
s6	We further discuss the low-frequency scattering of a charged scalar by a Kerr-Newman-AdS-dS black hole and find the dual CFT description.	contribution 0.86	0.96	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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arXiv listing abstract v3

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references and citing sentences
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The paper

Original abstract

In this paper, we study the holographic description of the generic four-dimensional non-extremal Kerr-Newman-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, there exists hidden conformal symmetry on the solution space. Similar to the Kerr case, this suggests that the Kerr-Newman-AdS-dS black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=\frac{6a(r_++r_\ast)}{k}$ and temperatures $T_L=\frac{k(r_+^2+r_\ast^2+2a^2)}{4\pi a\Xi(r_++r_\ast)}, T_R=\frac{k(r_+-r_\ast)}{4\pi a\Xi}$. The macroscopic Bekenstein-Hawking entropy could be recovered from the microscopic counting in dual CFT via the Cardy formula. Using the Minkowski prescription, we compute the real-time correlators of the scalar, photon and graviton in near horizon geometry of near extremal Kerr-AdS-dS black hole. In all these cases, the retarded Green's function and the corresponding absorption cross section are in perfect match with CFT prediction. We further discuss the low-frequency scattering of a charged scalar by a Kerr-Newman-AdS-dS black hole and find the dual CFT description.

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References

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Universal Entropy and Hawking Radiation of Near-Extremal AdS$_4$ Black Holes
hep-th 2020-09 conditional novelty 5.0 of 10

Near-extremal AdS4 electrically charged rotating black hole entropy is shown to equal S* plus (C/TH)_* times TH, with the same expression obtained from gravity, near-horizon Kerr/CFT, and boundary ABJM computations.
Exploring the BTZ bulk with boundary conformal blocks
hep-th 2016-04 conditional novelty 5.0 of 10

The radial position of a field in the BTZ black hole maps to a conformal cross-ratio in a transformed boundary CFT, allowing the bulk field to be extracted from a heavy-light Virasoro conformal block.
The Kerr-Newman metric: A Review
gr-qc 2014-10 accept novelty 2.0 of 10

The Kerr-Newman metric, describing a charged rotating black hole, can be derived from the Reissner-Nordstrom solution by a complex transformation and has a ring singularity, horizons, and an ergosphere.
The Kerr/CFT correspondence and its extensions: a comprehensive review
hep-th 2012-03 conditional novelty 2.0 of 10

A chiral half of Cardy's formula reproduces the Bekenstein-Hawking entropy of essentially every known extremal black hole, but the review argues no standard dual CFT exists.

How the literature uses it

22 arXiv papers cite this in 42 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 22 sentences without a confident label

Builds on it 2 papers

We showed that, besides the angular momentum $J$-picture (associated with the Kerr/CFT duality, where the central charges of the dual 2D CFT are $c_L = c_R = 12J$) revealed in [ref] , another $Q$-picture (associated with the RN/CFT duality, in which the central charges are $c_L = c_R = 6Q^3/ℓ$, where $ℓ$ is the parameter depends on the embedding) does exist for the general nonextremal KN black hole by probing the 2D hidden conformal symmetries via an external charged scalar field [ref] .

The Kerr-Newman/CFTs Correspondence · Introduction · 0.81
For the near-extremal case, [ref] initiated some progress and we extend those results here by computing the entropies of near-extremal AdS$_4$ black holes via the Cardy formula.

Universal Entropy and Hawking Radiation of Near-Extremal AdS$_4$ Black Holes · Near-Extremal AdS$_4$ Black Hole Entropy from Cardy Formula · 0.99

Uses its method or tool 3 papers

Based on hidden conformal symmetry [ref] , the right temperature is T_R = k (r_+ - r_s)/4 πa Ξ .

Universal Entropy and Hawking Radiation of Near-Extremal AdS$_4$ Black Holes · Near-Extremal AdS$_4$ Black Hole Entropy from Cardy Formula · 0.92
Similar to the treatment in [ref] , we need to focus on the near-horizon region.

Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole · Introduction · 0.94
Similar with the analysis in [ref] , we focus on the near-horizon region, where $r-r_+$ is a small quantity, so we can series $f_r^KNA Δ$ to the quadratic order, [equation] where $r_+$ always stands for outer horizon, and [equation]

Hidden Conformal Symmetry for Vector Field on Various Black Hole Backgrounds · Low frequency limit at Near-Horizon region · 0.91

Compares with it 2 papers

From ([ref]) and ([ref]), we obtain the central charge and the temperature directly c_L^J=6k(r_+^2+a^2)Ξ=12r_+(1-r_+^2/ℓ^2)(r_+^2+3r_+^4/ℓ^2-q^2) 1+6r_+^2/ℓ^2-3r_+^4/ℓ^4-q^2/ℓ^2, T_L^J=12πk T_L=(1+6r_+^2/ℓ^2-3r_+^4/ℓ^4-q^2/ℓ^2)(2r_+^2+2r_+^4/ℓ^2-q^2) 4πr_+(1-2r_+^2/ℓ^2-3r_+^4/ℓ^2+q^2/ℓ^2) (1-r_+^2/ℓ^2)(r_+^2+3r_+^4/ℓ^2-q^2),which are in perfect match with the result in [ref] .

Novel CFT Duals for Extreme Black Holes · J-picture · 0.97
It should be noted that, unlike the case of higher dimensional black holes [ref] , where the near-region limit for the radial wave equation is taken into account, in the present case, no extra approximation is needed to match the wave equation of scalar field with the Casimir operator.

Hidden Conformal Symmetry of Self-Dual Warped AdS_3 Black Holes in Topological Massive Gravity · SL(2, R)$_L×$SL(2, R)$_R$ · 0.86

Cites it as support 1 paper

We expect that a general scattering theory around any near-extremal black hole solution of [ref] will also be consistent with a CFT description, as supported by all cases studied beyond the Kerr-Newman black hole [ref] .

The Kerr/CFT correspondence and its extensions: a comprehensive review · Microscopic greybody factors · 0.97

Cites it as background 10 papers

The most notable such example is by far the Kerr/$CFT$ correspondence and its extensions [ref] , where the general idea is that the asymptotic symmetry group (ASG), preserving certain metric boundary or fall off conditions, is generated by a Virasoro algebra with calculable central extension: [equation] The Bekenstein-Hawking entropy is then obtained from Cardy's Formula [ref] in terms of $c$ and the proper normalized lowest eigen-mode via: [equation] In the Kerr/$CFT$ case a thermal Cardy Formula is employed [equation] which depends on the left Frolov-Thorne vacuum temperature $T_L$ for generic Kerr geometry [ref] .

Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality · Holographic Black Hole Entropy · 0.88
This concept is most notably exemplified by the $Kerr/CFT$ correspondence [ref] and its extensions [ref] .

Near-Extremal Black Hole Thermodynamics from AdS2/CFT1 Correspondence in The Low Energy Limit of 4D Heterotic String Theory · Introduction · 0.91
Following the introduction of the thermodynamic volume [ref] studies of the equation of state and phase transitions of AdS black holes have proceeded in a manner similiar from classical thermodynamics, for example by plotting isotherms on $P-V$ diagrams and utilizing the Gibbs free energy [ref] .

Cosmography of KNdS Black Holes and Isentropic Phase Transitions · Properties of Kerr-Newman deSitter black holes · 0.80

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