scholarly journals Entropy of (2+1) dimensional de Sitter space in terms of the brick wall method

1999 ◽  
Vol 59 (4) ◽  
Author(s):  
Won Tae Kim
Keyword(s):  
De Sitter Space ◽  
Brick Wall ◽  
De Sitter ◽  
Wall Method

THE ENTROPY CALCULATED VIA BRICK-WALL METHOD COMES FROM A THIN FILM NEAR THE EVENT HORIZON

2001 ◽  
Vol 16 (23) ◽  
pp. 3793-3803 ◽  
Author(s):  
WENBIAO LIU ◽  
ZHENG ZHAO
Keyword(s):  
Thin Film ◽  
Black Hole ◽  
Event Horizon ◽  
Fundamental Problem ◽  
Dirac Field ◽  
Brick Wall ◽  
De Sitter ◽  
Wall Model ◽  
Mass Approximation ◽  
Wall Method

The brick-wall method put forward by 't Hooft has contributed a great deal to the understanding and calculating of the entropy of a black hole. However, there are some drawbacks in it such as little mass approximation, neglecting logarithm terms, and taking the term including L3 as a contribution of the vacuum surrounding the black hole. Moreover, the fundamental problem is why the entropy of scalar field or Dirac field surrounding a black hole is the entropy of the black hole itself. It is well known that the event horizon is the characteristic of a black hole. The entropy calculation of a black hole should be only related to its horizon. Due to this analysis, we improve the brick-wall model by taking that the entropy of a black hole is only contributed by a thin film near the event horizon. This improvement not only gives us a satisfied result, but also avoids the drawbacks in the original brick-wall method. It is found that there is an intrinsic relation between the event horizon and the entropy. We also calculate the entropy of Schwarzschild–de Sitter space–time via the improved method, which can hardly be resolved via the original model.

ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM

2001 ◽  
Vol 16 (11) ◽  
pp. 719-723 ◽  
Author(s):  
REN ZHAO ◽  
JUNFANG ZHANG ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Thermal Equilibrium ◽  
Gordon Equation ◽  
Brick Wall ◽  
De Sitter ◽  
Logarithmic Term ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wall Method

Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

DIVERGENCE STRUCTURE FOR THE STATISTICAL ENTROPY OF SPIN FIELDS IN REISSNER–NORDSTRÖM–de SITTER SPACE–TIME

2002 ◽  
Vol 17 (14) ◽  
pp. 887-897 ◽  
Author(s):  
ZHONG-HENG LI
Keyword(s):  
Scalar Fields ◽  
De Sitter Space ◽  
Space Time ◽  
Brick Wall ◽  
De Sitter ◽  
Statistical Entropy ◽  
Wall Model ◽  
Thin Region ◽  
Spin Fields ◽  
Divergence Structure

We consider the divergences at all levels for the statistical entropy of gravitational, electromagnetic, neutrino and scalar fields on extremal and nonextremal Reissner–Nordström–de Sitter space–time background in terms of the brick-wall model. We find that entropy of spin fields within a region near coinciding horizons has higher divergence than usual. The earlier result that the entropy of spin fields is proportional to scalar one or the horizon area holds only for the thin region near an isolated horizon, since the spin-dependent divergences exist in all other cases.

ENTROPY OF SCALAR FIELDS IN REISSNER–NORDSTRÖM–(ANTI-)DE SITTER SPACETIMES

1996 ◽  
Vol 11 (25) ◽  
pp. 2027-2036 ◽  
Author(s):  
RONG-GEN CAI ◽  
YUAN-ZHONG ZHANG
Keyword(s):  
Black Holes ◽  
Naked Singularity ◽  
Scalar Fields ◽  
De Sitter Space ◽  
Brick Wall ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Sitter Background

The entropy of a free scalar field is calculated in the Reissner–Nordström–(anti-)de Sitter spacetimes. Due to the presence of the cosmological horizon in the Reissner–Nordström–de Sitter spacetime, we introduce a cutoff at the cosmological horizon, besides the cutoff at the horizon of black holes in the brick wall model. The entropy is found to be the sum of two terms, which are proportional to the area of the cosmological horizon and of black hole horizon, respectively. In the Reissner–Nordström–anti-de Sitter spacetime the contribution of the anti-de Sitter background to the entropy of scalar fields vanishes when an infinite volume is taken. The entropy of scalar fields is also evaluated in some special backgrounds described by solutions of Einstein–Maxwell equations with a cosmological constant, such as the cold black holes, lukewarm black holes, ultracold solutions, a naked singularity in de Sitter space, and the de Sitter space. The physical meaning of some results is briefly discussed.

BLACK HOLE ENTROPY FOR ANTI DE SITTER AND DE SITTER DILATONIC SPACETIME USING BRICK WALL METHOD

2007 ◽  
Vol 22 (37) ◽  
pp. 2865-2872 ◽  
Author(s):  
TANWI GHOSH
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Semiclassical Approach ◽  
Sitter Spacetime ◽  
Dilatonic Black Hole ◽  
Finite Result ◽  
Wall Method

The entropy of a scalar field in the background of a dilatonic black hole both in anti de Sitter and de Sitter spacetime has been calculated using brick wall method. The form of divergent contributions to the entropy is in agreement with the previous calculations in the literature. The semiclassical approach used here is straightforward and produces finite result apart from an ambiguity in logarithmic terms.

scholarly journals Gravitational turbulent instability of anti-de Sitter space

2012 ◽  
Vol 29 (19) ◽  
pp. 194002 ◽  
Author(s):  
Óscar J C Dias ◽  
Gary T Horowitz ◽  
Jorge E Santos
Keyword(s):  
De Sitter Space ◽  
De Sitter

scholarly journals Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Samim Akhtar ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Debopam Goswami ◽  
Sudhakar Panda ◽  
...  
Keyword(s):  
Scalar Field ◽  
Density Matrix ◽  
Master Equation ◽  
Quantum Entanglement ◽  
De Sitter Space ◽  
Thermal Bath ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Open Quantum ◽  
Non Locality

Abstract In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$$e'$$e′nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.

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