Black hole entropy, curved space and monsters

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.

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MONSTERS, BLACK HOLES AND THE STATISTICAL MECHANICS OF GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732309031624 ◽

2009 ◽

Vol 24 (24) ◽

pp. 1875-1887 ◽

Cited By ~ 17

Author(s):

STEPHEN D. H. HSU ◽

DAVID REEB

Keyword(s):

Black Hole ◽

Statistical Mechanics ◽

Black Hole Entropy ◽

Flat Space ◽

Equal Mass ◽

Effective Field ◽

Curved Space ◽

Recent Developments ◽

Proper Volume ◽

Theory Framework

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective, they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics — essentially, the geometry of Hilbert space — and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.

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Reply to Pessoa, P.; Arderucio Costa, B., Comment on “Tsallis, C. Black Hole Entropy: A Closer Look. Entropy 2020, 22, 17”

Entropy ◽

10.3390/e23050630 ◽

2021 ◽

Vol 23 (5) ◽

pp. 630

Author(s):

Constantino Tsallis

Keyword(s):

Black Hole ◽

Black Hole Entropy ◽

Comment on “Black Hole Entropy from Conformal Field Theory in Any Dimension”

Physical Review Letters ◽

10.1103/physrevlett.83.5595 ◽

1999 ◽

Vol 83 (26) ◽

pp. 5595-5595 ◽

Cited By ~ 43

Author(s):

Mu-In Park ◽

Jeongwon Ho

Keyword(s):

Field Theory ◽

Black Hole ◽

Conformal Field Theory ◽

Black Hole Entropy ◽

Conformal Field

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THE BLACK HOLE ENTROPY BOUND AND THE MAXIMUM TEMPERATURE FOR MESON FORMATION IN THE NUCLEAR FIREBALL

Modern Physics Letters A ◽

10.1142/s0217732391003535 ◽

1991 ◽

Vol 06 (33) ◽

pp. 3039-3045 ◽

Cited By ~ 4

Author(s):

JISHNU DEY ◽

MIRA DEY ◽

MARCELO SCHIFFER ◽

LAURO TOMIO

Keyword(s):

Black Hole ◽

Simple Model ◽

Black Hole Entropy ◽

Heavy Ion ◽

Black Hole Thermodynamics ◽

Maximum Temperature ◽

Ion Collisions ◽

Pion Interferometry ◽

Entropy Bound ◽

Confined System

The entropy bound from black hole thermodynamics can be invoked to set limits for temperatures at which hadrons can survive as a confined system. We find that this implies that the pion can be formed in heavy ion collisions, much later than heavier mesons, for example the ρ-meson, when the fireball is cooler. The temperature found in a simple model agree qualitatively with experiment. We also suggest that this may be the reason why in pion interferometry experiments the space-time volume of the pion source seems large.

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