Near-horizon conformal symmetry and black hole entropy in any dimension

Kang, G.; Koga, Jun-ichirou; Park, Mu-In

doi:10.1103/physrevd.70.024005

Cited by 57 publications

(68 citation statements)

References 39 publications

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“…It follows that the local conformal algebra acts on solution space as 24) and with δϕ = 0. Note that the overall minus sign is convential and choosen so that…”

Section: Conformal Properties Of Solution Spacementioning

confidence: 99%

“…More recently, a similar analysis has been used to derive the Bekenstein-Hawking entropy of an extreme 4-dimensional Kerr black hole [13]. One of our hopes is to make progress along these lines in the non extreme case, either directly from an analysis at null infinity or by making a similar analysis at the horizon, as discussed previously for instance in [14,15,16,17,18,19,20,21,22,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

“…is interesting as it turnsγ AB into the flat metric on the Riemann sphere with vanishing Christoffel symbols,γ 24) with T = P T . In terms of T , we get instead of the last of (4.11)…”

Section: Besides the Previous Conditions That Ymentioning

confidence: 99%

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Aspects of the BMS/CFT correspondence

Barnich

Troessaert

2010

J. High Energ. Phys.

591

967

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ABSTRACT. After a review of symmetries and classical solutions involved in the AdS 3 /CFT 2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi's news tensor, mass and angular momentum aspects under local conformal transformations.

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“…It follows that the local conformal algebra acts on solution space as 24) and with δϕ = 0. Note that the overall minus sign is convential and choosen so that…”

Section: Conformal Properties Of Solution Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aspects of the BMS/CFT correspondence

Barnich

Troessaert

2010

J. High Energ. Phys.

591

967

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“…The null limit of this formulation is usually singular and the null normal does not have a unique normalization. Moreover, the result seems to depend on the horizon boundary conditions [25,26] and the constraint algebra is complicated by the appearance of additional constraints related to the use of a null frame in the slicing [23].Apart from these technical difficulties, derivations that use near-horizon symmetries leave unanswered the question about the localization of the microstates responsible for the black hole entropy. A number of cases are known for which the Bekenstein-Hawking entropy can be reproduced using a conformal filed theory (CFT) living either on the black hole horizon or on a timelike asymptotical boundary of the spacetime [13,14,15,16,17].…”

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confidence: 99%

Statistical Entropy of the Schwarzschild Black Hole

Cadoni

2006

Mod. Phys. Lett. A

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We derive the statistical entropy of the Schwarzschild black hole by considering the asymptotic symmetry algebra near the I − boundary of the spacetime at past null infinity. Using a two-dimensional description and the Weyl invariance of black hole thermodynamics this symmetry algebra can be mapped into the Virasoro algebra generating asymptotic symmetries of anti-de Sitter spacetime. Using lagrangian methods we identify the stress-energy tensor of the boundary conformal field theory and we calculate the central charge of the Virasoro algebra. The Bekenstein-Hawking result for the black hole entropy is regained using Cardy's formula. Our result strongly supports a non-local realization of the holographic principle Black holes can be understood as thermodynamical systems with characteristic temperature and entropy [1,2]. In the last decade a lot of effort has been devoted to understand the microscopic origin of black hole thermodynamics. A detailed microscopical explanation of the thermodynamical properties of black holes would represent not only an important tool for understanding the quantum behavior of gravity but also a way to give a fundamental meaning to the holographic principle [3,4]. A variety of approaches have been used to explain the microscopical origin of the Bekenstein-Hawking entropy: string theoretical (D-Brane) approaches [5,6,7,8,9], methods based on loop quantum gravity [10], induced gravity [11,12], asymptotic symmetries [13,14,15,16,17,18,19,20,21,22,23] and canonical quantization [24]. None of these derivations can be considered as completely satisfactory. In some cases the computation works only for a restrict class of solutions, e.g supersymmetric or asymptotically Anti-de Sitter (AdS) solutions. In other cases the origin of the microscopic degrees of freedom responsible for the black hole entropy is completely obscure. Nonetheless, the fact that completely independent methods give more or less the same (right) answer strongly indicates that the computation of the statistical black hole entropy can be performed without detailed knowledge of the physics governing the microscopical degrees of freedom.If this is the case the statistical black hole entropy should be explained in terms of fundamental features (e.g symmetries) of the "emergent" classical theory of gravity of which black holes are solutions. The most natural realization of this scenario is represented by near-horizon conformal symmetries controlling the black hole entropy trough Cardy's formula for the density of states [21,23]. Carlip has pointed out the main ingredients to be used in this approach: a) Near-horizon conformal symmetries, b) Asymptotic symmetries, c) Canonical realization of the symmetries, d) Horizon constraints [21]. However, the approach of Carlip has some drawbacks. To avoid the complications of the Hamiltonian formulation with a null slicing one has to consider a distorted, "almost" null, horizon [21,23]. The null limit of this formulation is usually singular and the null normal does not have a unique normal...

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“…Another approach which has been very useful in black hole entropy analysis is based on the existence of a CFT in the near-horizon region of black holes [2,17,18,19]. The analysis here is also based on Brown and Henneaux's approach [12], suitably adapted to the near-horizon region.…”

Section: Introductionmentioning

confidence: 99%

Universal Near-Horizon Conformal Structure and Black Hole Entropy

Chakrabarti

Gupta

Sen

2008

Int. J. Mod. Phys. A

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It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.

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Near-horizon conformal symmetry and black hole entropy in any dimension

Cited by 57 publications

References 39 publications

Aspects of the BMS/CFT correspondence

Aspects of the BMS/CFT correspondence

Statistical Entropy of the Schwarzschild Black Hole

Universal Near-Horizon Conformal Structure and Black Hole Entropy

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