Statistical mechanics of gravitons in a box and the black hole entropy

Abstract

This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index $\ell$ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy $<E>$ results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole internal energy $U$ is provided by its ADM rest energy, without invoking particular quantum gravity theories. This seriously suggests that the interior of a black hole can be composed of trapped gravitons at a thermodynamical temperature proportional by a factor $\simeq 2$ to the horizon temperature $T_h$.

Version published on PHYSICA A

References in corpus (4)

• Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
• Black hole entropy from graviton entanglement
• Is the Rindler horizon energy nonvanishing ?
• A statistical representation of the cosmological constant from finite size effects at the apparent horizon

Cited by in corpus (6)

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• Gravitons in a Casimir box
• On the perturbative formalism and a possible quantum discrete spectrum for the Regge-Wheeler equation of a de Sitter spacetime
• Vapor Pressure in a Paramagnetic Solid?
• Corrections to the Black hole entropy from a Bose Einstein condensate: a semi-classical phenomenological approach