Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy
Abstract
In this paper we study the proposal present in Viaggiu (2017) concerning the statistical description of trapped gravitons and applied to derive the semiclassical black hole (BH) entropy S_{BH}. We study the possible configurations depending on physically reasonable expressions for the internal energy U. In particular, we show that expressions for U ∼R^{k} , k ≥ 1, with R the radius of the confining spherical box, can have a semiclassical description, while behaviors with k < 1 derive from thermodynamic or quantum fluctuations. There, by taking a suitable physically motivated expression for U(R) , we obtain the well known logarithmic corrections to the BH entropy, with the usual behaviors present in the literature of BH entropy. Moreover, a phase transition emerges with a positive specific heat C at Planckian lengths instead of the usual negative one at nonPlanckian scales, in agreement with results present in the literature. Finally, we show that evaporation stops at a radius R of the order of the Planck length.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 December 2017
 DOI:
 10.1016/j.physa.2017.07.009
 arXiv:
 arXiv:1707.06785
 Bibcode:
 2017PhyA..488...72V
 Keywords:

 Trapped gravitons;
 Thermodynamic;
 Black hole entropy;
 Internal energy;
 Gravitational waves;
 Non commutative quantum spacetime;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Accepted for publication on Physica A