Holographic entropy bound in higher-dimensional spacetimes

Hod, Shahar

doi:10.1103/physrevd.97.126012

Cited by 3 publications

(8 citation statements)

References 19 publications

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“…(61). It is further conjectured that the bound also holds for higher d-dimensions, with the area A being a d − 2 surface A enclosing a d − 1 volume [33].…”

Section: Euler Relationmentioning

confidence: 98%

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Thermodynamics and entropy of self-gravitating matter shells and black holes in d dimensions

2019

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The thermodynamic properties of self-gravitating spherical thin matter shells an black holes in d > 4 dimensions are studied, extending previous analysis for d = 4. The shell joins a Minkowski interior to a Tangherlini exterior, i.e., a Schwarzschild exterior in d dimensions, with d 4, The junction conditions alone together with the first law of thermodynamics enable one to establish that the entropy of the thin shell depends only on its own gravitational radius. Endowing the shell with a well-defined power-law temperature equation of state allows to establish a precise form for the entropy and to perform a thermodynamic stability analysis for the shell. A particularly interesting case is when the shell's temperature has the Hawking form, i.e., it is inversely proportional to the shell's gravitational radius. It is shown in this case that the shell's heat capacity is positive, and thus the shell is stable, for shells with radii in-between their own gravitational radius and the photonic radius, i.e., the radius of circular photon orbits, reproducing unexpectedly York's thermodynamic stability criterion for a d = 4 black hole in the canonical ensemble. Additionally, the Euler equation for the matter shell is derived, the Bekenstein and holographic entropy bounds are studied, and the large d limit is analyzed. Within this formalism the thermodynamic properties of black holes can be studied too. Putting the shell at its own gravitational radius, i.e., in the black hole situation, obliges one to choose precisely the Hawking temperature for the shell which in turn yields a black hole with the Bekenstein-Hawking entropy. The stability analysis implies that the black hole is thermodynamically stable substantiating that in this configuration our system and York's canonical ensemble black hole are indeed the same system. Also relevant is the derivation in a surprising way of the Smarr formula for black holes in d dimensions.

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“…(61). It is further conjectured that the bound also holds for higher d-dimensions, with the area A being a d − 2 surface A enclosing a d − 1 volume [33].…”

Section: Euler Relationmentioning

confidence: 98%

“…We adopt the thermodynamic formalism presented in [29]. We also study the Bekenstein [30] and the holographic [31][32][33] entropy bounds for the d-dimensional shells. We benefit from the result given in [34] where it is shown that to be divergent free quantically black holes must be at the Hawking temperature.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and entropy of self-gravitating matter shells and black holes in d dimensions

2019

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“…Moreover, semiclassical aspects of black hole physics at large D have been a direct focus of [6][7][8][9]. In particular, the Hawking luminosity was explicitly found in [6], and Refs.…”

Section: Connection To Previous Workmentioning

confidence: 99%

“…In particular, the Hawking luminosity was explicitly found in [6], and Refs. [7][8][9] have discussed the relative size of black hole entropy as compared to the entropies of unbound systems of weakly gravitating matter at large D.…”

Section: Connection To Previous Workmentioning

confidence: 99%

“…Recent studies of the limit of a large number of spacetime dimensions D have led to a better understanding of the aspects of classical general relativity, especially for black holes [4,5]. Yet, semiclassical (and fully quantum) features of black holes [6][7][8][9] within these new formulations of this large-D limit seem to be relatively unexplored. This paper is yet another partial step in this direction.…”

Section: Introductionmentioning

confidence: 99%

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Black hole evaporation and semiclassicality at large D

Holdt-Sørensen¹,

McGady

Wintergerst³

2020

Phys. Rev. D

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Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small, and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large D, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds come from demanding that the rate of change of the geometry is small and that black holes scramble information faster than they evaporate. This is a consequence of the enormous power of Hawking radiation in D dimensions due to the large available phase space and the resulting minuscule evaporation times. Asymptotically, only black holes with entropies S ≥ D Dþ3 log D are semiclassical. We comment on implications for realistic quantum gravity models in D ≤ 26 as well as relations to bounds on theories with a large number of gravitationally interacting light species.

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Black hole evaporation and semiclassicality at large D

Holdt-Sørensen,

McGady,

Wintergerst

2019

Preprint

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Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large D, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds come from demanding that the rate of change of the geometry is small and that black holes scramble information faster than they evaporate. This is a consequence of the enormous power of Hawking radiation in D-dimensions due to the large available phase space and the resulting minuscule evaporation times. Asymptotically, only black holes with entropies S ≥ D D+3 log D are semiclassical. We comment on implications for realistic quantum gravity models in D ≤ 26 as well as relations to bounds on theories with a large number of gravitationally interacting light species.

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Holographic entropy bound in higher-dimensional spacetimes

Cited by 3 publications

References 19 publications

Thermodynamics and entropy of self-gravitating matter shells and black holes in d dimensions

Thermodynamics and entropy of self-gravitating matter shells and black holes in d dimensions

Black hole evaporation and semiclassicality at large D

Black hole evaporation and semiclassicality at large D

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