Mass and charge fluctuations and black hole entropy

TL;DR

This paper investigates how thermal fluctuations in mass and charge affect the entropy of non-rotating charged black holes, revealing a universal logarithmic correction and analyzing the interplay between quantum and thermal effects.

Contribution

It introduces a model for black hole entropy corrections due to thermal fluctuations, showing a universal logarithmic term independent of specific mass-area relations.

Findings

Logarithmic correction to entropy with positive coefficient

Fluctuations of mass and charge are independent of mass-area relation details

Potential cancellation between quantum and thermal entropy corrections

Abstract

The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of non-rotating charged {\it macroscopic} black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to {\it fixed area} quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.