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 ℓ 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 BekensteinHawking 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 ≃ 2 to the horizon temperature T_{h}.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 May 2017
 DOI:
 10.1016/j.physa.2017.01.052
 arXiv:
 arXiv:1701.06193
 Bibcode:
 2017PhyA..473..412V
 Keywords:

 Statistical mechanics;
 Gravitational waves;
 Gravitons;
 Black hole entropy;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Version published on PHYSICA A