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arXiv · 1701.06193

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

Stefano Viaggiu
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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 $ $ 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 $T_h$.

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Stefano Viaggiu. 2017-01-22. Statistical mechanics of gravitons in a box and the black hole entropy. https://doi.org/10.1016/j.physa.2017.01.052

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