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 $T_h$.

arXiv commentVersion published on PHYSICA A

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• The cosmological constant from Planckian fluctuations and the averaging procedure
• The spectrum of the Schrödinger Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions
• Gravitons in a Casimir box
• The physical origin of the cosmological constant: continuum limit and the analogy with the Casimir effect
• On the perturbative formalism and a possible quantum discrete spectrum for the Regge-Wheeler equation of a de Sitter spacetime
• Corrections to the Black hole entropy from a Bose Einstein condensate: a semi-classical phenomenological approach
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