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Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy

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  • Viaggiu, Stefano

Abstract

In this paper we study the proposal present in Viaggiu (2017) concerning the statistical description of trapped gravitons and applied to derive the semi-classical black hole (BH) entropy SBH. We study the possible configurations depending on physically reasonable expressions for the internal energy U. In particular, we show that expressions for U∼Rk,k≥1, with R the radius of the confining spherical box, can have a semi-classical 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 non-Planckian 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.

Suggested Citation

  • Viaggiu, Stefano, 2017. "Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 72-84.
    • Handle: RePEc:eee:phsmap:v:488:y:2017:i:c:p:72-84
    DOI: 10.1016/j.physa.2017.07.009
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