An operational approach to black hole entropy

Pretorius, Frans; Vollick, Dan N.; Israel, W.

doi:10.1103/physrevd.57.6311

Cited by 46 publications

(110 citation statements)

References 17 publications

(14 reference statements)

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“…[7] and using the definition (12), one can see that there is only one singularity in C R (see Fig. 2).…”

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confidence: 99%

“…We shall compare our results and extend the evaluation of the specific heats with the approach of Ref. [7] and comment on other references [6,7], where different choices for the definition of the thermodynamical observables are employed.…”

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confidence: 99%

“…The properties of the system depend on the equation of state, that is a relation between the thermodynamically independent quantities. In order to obtain some explicit results we shall consider the general case of a power-law dependence of the shell temperature (introduced as usual through the second law of thermodynamics) on the inner horizon radius and also examine the particular choice corresponding to the Hawking temperature of the incipient black hole or other choices [7]. We use units for which = c = k B = 1, with k B the Boltzmann constant.…”

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confidence: 99%

“…Finally, one may also consider the "operational" approach to black hole entropy, as illustrated in Ref. [7], which leads one to the conclusion that the entropy of a black hole is the same as that stored in a shell of matter sitting just outside its Schwartzschild radius after it has collapsed from infinity. According to the AdS-CFT correspondence, a black hole is represented by a thermal state and its formation by the approach to such a state.…”

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confidence: 99%

“…In Ref. [7] a basic statement is that the temperature attributed to the shell is that of a static observer standing just outside the shell, that is…”

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confidence: 99%

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Thermodynamics of a collapsing shell in an expanding universe

2004

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We describe the quasi-static collapse of a radiating, spherical shell of matter in de Sitter space-time using a thermodynamical formalism. It is found that the specific heat at constant area and other thermodynamical quantities exhibit singularities related to phase transitions during the collapse.Because of the paradigm of inflation, de Sitter space-time has recently become the subject of great research interest. One aspect of research has been the conjectured dS-CFT correspondence [1] which is the analogue of Maldacena's AdS-CFT conjecture [2] for the case of a spacetime with a positive cosmological constant. As in the latter case, the "gravitational" (dS) side of the correspondence is expected to yield the macroscopic description of the system, whereas the CFT (conformal field theory) should be able to describe the microphysics. A well known example for the AdS-CFT is given by the microscopical description of the thermodynamical laws of black holes [3]. Furthermore, applications of the de Sitter space Bousso bound [4], related to the Bekenstein bound for flat space-times, have also drawn much interest.The dS-CFT correspondence has not yet reached the degree of comprehension of the AdS-CFT, since the corresponding CFT has not been completely identified. Therefore, one usually proceeds by studying simplified "gravitational" models in order to obtain general features that the relevant CFT is required to possess. One such model is given by a thin spherical shell of matter in a de Sitter space-time, since it may represent a collection of D-branes forming the so called D-Sitter space-time of Ref. [5], or can be used as a tool for the study of the entropy bound in a very simplified physical environment [6]. Finally, one may also consider the "operational" approach to black hole entropy, as illustrated in Ref. [7], which leads one to the conclusion that the entropy of a black hole is the same as that stored in a shell of matter sitting just outside its Schwartzschild radius after it has collapsed from infinity. According to the AdS-CFT correspondence, a black hole is represented by a thermal state and its formation by the approach to such a state. A thermodynamical description of the gravitational collapse should thus be useful in the de Sitter case as well. *

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“…[7] and using the definition (12), one can see that there is only one singularity in C R (see Fig. 2).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…In Ref. [7] a basic statement is that the temperature attributed to the shell is that of a static observer standing just outside the shell, that is…”

mentioning

confidence: 99%

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Thermodynamics of a collapsing shell in an expanding universe

2004

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Accelerated Observers, Thermal Entropy, and Spacetime Curvature

Kothawala

2017

Gravity and the Quantum

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Assuming that an accelerated observer with four-velocity u u u R in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", I show that the change in horizon area under parametric displacements of the horizon has a very specific thermodynamic structure. Specifically, it entails information about the time-time component of the Einstein tensor: G G G(u u u R , u u u R ). Demanding that the result holds for all accelerated observers, this actually becomes a statement about the full Einstein tensor, G G G.I also present some perspectives on the free fall with four-velocity u u u ff across the horizon that leads to such a loss of entropy for an accelerated observer. Motivated by results for some simple quantum systems at finite temperature T , we conjecture that at high temperatures, there exists a universal, system-independent curvature correction to partition function and thermal entropy of any freely falling system, characterised by the dimensionless quantity ∆ = R R R(u u u ff , u u u ff ) (hc/kT ) 2 . Gravity and ThermodynamicsIt has been well known for a long time that statistical mechanics in presence of gravitational interactions exhibits several peculiar features [1], deriving mostly from the fact that gravity couples to everything, and operates unshielded with an infinite range. Many of these peculiarities, such as negative specific heat, however, attracted attention only after they were encountered in the context of black holes. Indeed, existence of a horizon magnifies quantum effects in presence of a black hole, re-

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Membrane paradigm and horizon thermodynamics in Lanczos-Lovelock gravity

Kolekar

Kothawala

2012

J. High Energ. Phys.

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We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients η and ζ of the membrane fluid. We show that the membrane pressure is intimately connected with Noether charge entropy S Wald of the horizon when we consider a specific mth order Lanczos-Lovelock model, through the relation p (m) A/T = [(D − 2m)/(D − 2)] S (m) Wald , where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation ζ = −2(D − 3)/(D − 2)η.

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An operational approach to black hole entropy

Cited by 46 publications

References 17 publications

Thermodynamics of a collapsing shell in an expanding universe

Thermodynamics of a collapsing shell in an expanding universe

Accelerated Observers, Thermal Entropy, and Spacetime Curvature

Membrane paradigm and horizon thermodynamics in Lanczos-Lovelock gravity

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