Bekenstein bounds in de Sitter and flat space

Bousso, Raphael

doi:10.1088/1126-6708/2001/04/035

Cited by 120 publications

(172 citation statements)

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“…This inequality is obtained by considering the classical absorption of the system by a large black hole; it does not depend on the dimension of spacetime [6]. Bekenstein's bound is remarkably tight (consider, for example, a massive particle in a box the size of its Compton wavelength).…”

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Light Sheets and Bekenstein’s Entropy Bound

Bousso

2003

Phys. Rev. Lett.

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From the covariant bound on the entropy of partial light-sheets, we derive a version of Bekenstein's bound: S/M ≤ πx/h, where S, M , and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light-sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.Entropy bounds have undergone a remarkable transformation from a corollary to a candidate for a first principle [1]. After proposing the generalized second law of thermodynamics (GSL) [2,3]-that the sum of black hole entropy and ordinary matter entropy never decreasesBekenstein argued that its validity necessitates a modelindependent bound [4,5] on the entropy S of weakly gravitating systems:where M is the total gravitating energy, and d is the linear size of the system, defined to be the diameter of the smallest sphere that fits around the system. This inequality is obtained by considering the classical absorption of the system by a large black hole; it does not depend on the dimension of spacetime [6]. Bekenstein's bound is remarkably tight (consider, for example, a massive particle in a box the size of its Compton wavelength). It has appeared in discussions ranging from information technology to quantum gravity. Since M ≪ d/4G for a weakly gravitating system, it also implies the "spherical entropy bound",Here A cs is the area of the circumscribing sphere. Though confined to weak gravity, 't Hooft [7] and Susskind [8] ascribed fundamental significance to Eq. (2), claiming that it reflects a non-extensivity of the number of degrees of freedom in nature. This eventually prompted the conjecture of a more general bound, the covariant entropy bound [9]. Empirically, this bound has been found to hold in large classes of examples, including systems in which gravity is the dominant force. Meanwhile, no violation has been observed, nor have any theoretical counterexamples been constructed from a realistic effective theory of matter and gravitation.Although the covariant bound does not conflict with the phenomenology of our present models, it cannot be derived from known principles. It may be interpreted as an unexplained pattern in nature, betraying a fundamental relation between information and spacetime geometry.Then the bound must eventually be explained by a unified theory of gravity, matter, and quantum mechanics. In the mean time, it should be regarded as providing important hints about such a theory.We are thus motivated to consider the covariant entropy bound primary, and to try to derive other laws of physics from it. As we will shortly discuss, the bound has already been shown to imply the GSL, as well as older, more specialized entropy bounds. However, the oldest (and, for weakly gravitating systems, tightest...

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Light Sheets and Bekenstein’s Entropy Bound

Bousso

2003

Phys. Rev. Lett.

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“…A year later Hawking found a quantum evaporation of a black hole [3,4] which gave the birth to thermodynamics of black holes [5][6][7] (for a review see [8]). In 1976 Gibbons and Hawking found that also cosmological horizon can radiate [9], and this gave rise to thermodynamics of horizons [10][11][12][13][14][15][16][17][18].…”

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confidence: 99%

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

Dymnikova

Korpusik

2011

Entropy

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Abstract:We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGT μ ν = Λδ μ ν as r → 0, 8πGT μ ν = λδ μ ν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter M cr1 ≤ M ≤ M cr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon r c , a black hole horizon r b < r c , and an internal horizon r a < r b , which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basic features of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q = Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon r b and cosmological horizon r c . We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (r a = r b ) remnant with the positive specific heat and zero temperature.

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Section: Introductionmentioning

confidence: 99%

“…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.…”

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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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Bekenstein bounds in de Sitter and flat space

Cited by 120 publications

References 24 publications

Light Sheets and Bekenstein’s Entropy Bound

Light Sheets and Bekenstein’s Entropy Bound

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

Thermodynamics of a collapsing shell in an expanding universe

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