scholarly journals ENTROPY OF THE THREE-DIMENSIONAL SCHWARZSCHILD–de SITTER BLACK HOLE

2001 ◽  
Vol 16 (36) ◽  
pp. 2353-2357 ◽  
Author(s):  
Y. S. MYUNG
Keyword(s):  
Black Hole ◽  
Central Charge ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter ◽  
Correct Definition ◽  
Conical Defect ◽  
Entropy Bounds ◽  
Definition Of ◽  
Cardy Formula

We study the three-dimensional Schwarzschild–de Sitter ( SdS 3) black hole which corresponds essentially to a conical defect. We compute the mass of the SdS 3 black hole from the correct definition of the mass in asymptotically de Sitter space. Then we clarify the relation between the mass, entropy and temperature for this black hole without any ambiguity. We also establish the SdS 3/ CFT 2-correspondence for the entropy by applying the Cardy formula to a CFT with a central charge c = 3ℓ/2G3. Finally we discuss the entropy bounds for the SdS 3 black hole.

scholarly journals The central charge in three-dimensional anti-de Sitter space

1999 ◽  
Vol 16 (6) ◽  
pp. 1733-1736 ◽  
Author(s):  
Maximo Bañados ◽  
Miguel E Ortiz
Keyword(s):  
Central Charge ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter

scholarly journals STRINGS IN AdS3 AND THE SL(2, R) WZW MODEL

2001 ◽  
Vol 16 (05) ◽  
pp. 677-682
Author(s):  
HIROSI OOGURI
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Partition Function ◽  
Long Strings ◽  
Three Dimensional ◽  
De Sitter Space ◽  
De Sitter ◽  
Btz Black Hole ◽  
Discrete States ◽  
The One

Strings in the three-dimensional anti-de Sitter space in the NS background is described by the SL(2, R) WZW model. We present a complete description of the Hilbert space of the model. We then compute the one-loop partition function for Euclidean BTZ black hole backgrounds or equivalently thermal AdS3 backgrounds which are quotients of Euclidean AdS3. We see long strings and discrete states in agreement with the structure of the Hilbert space.

scholarly journals Central charges for AdS black holes

2021 ◽  
Author(s):  
Malcolm Perry ◽  
Maria J Rodriguez
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Central Charge ◽  
Negative Cosmological Constant ◽  
Ads Black Holes ◽  
Kerr Black Holes ◽  
Distinguishing Features ◽  
Area Law ◽  
Cardy Formula

Abstract Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a left-right pair of Virasoro algebras with associated charges that reproduce the Bekenstein-Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with cL = cR. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

2020 ◽  
Vol 29 (07) ◽  
pp. 2050048
Author(s):  
Xin-Yang Wang ◽  
Yi-Ru Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Dynamical Variable ◽  
De Sitter ◽  
The One ◽  
Definition Of ◽  
Spherically Symmetry ◽  
Interior Volume

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

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