Corrections to the Black hole entropy from a Bose Einstein condensate: a semi-classical phenomenological approach

TL;DR

This paper derives logarithmic corrections to black hole entropy within a Bose Einstein condensate model of gravitons, supporting the idea that black hole interiors may be composed of such condensates, using semi-classical and quantum mechanical arguments.

Contribution

It introduces a method to incorporate logarithmic corrections into black hole entropy based on a BEC of gravitons, advancing the understanding of black hole microstates.

Findings

Logarithmic corrections to Bekenstein-Hawking entropy are derived.

The entropy of a Planck-scale black hole is approximately 2πk_B.

The BEC model of gravitons is a viable description of black hole interiors.

Abstract

In this paper we obtain logarithmic corrections to the black hole entropy. Motivated by our recent proposal concerning the nature of the degrees of freedom leading to the black hole entropy in terms of a Bose Einstein (BEC) condensate of gravitons, we study how to introduce logarithmic corrections. In fact we show that, after modifying the internal energy by means of simple by physically sound arguments dictated by ordinary quantum mechanics and possible non-commutative effects at Planckian scales, a logarithmic term does appear in the Bekenstein Hawking entropy law. We also obtain that the entropy $S_{BH}$ of a ball of Planckian areal radius is $2\pi K_B$, i.e. $S_{BH}(R=L_P)=2\pi K_B$. Our approach show that the possibility that the interior of a black hole is composed with a BEC of gravitons is a viable physically motivated possibility.