On the Microcanonical Entropy of a Black Hole

TL;DR

This paper investigates the microcanonical entropy of black holes, testing the accuracy of logarithmic corrections to canonical entropy through analytical and numerical analysis of simplified models.

Contribution

It provides a detailed comparison of entropy calculations in models with quantum spectra, confirming the presence of a ln A correction term in black hole entropy.

Findings

Logarithmic correction accurately reproduces entropy in models

Leading entropy term proportional to horizon area A

Next correction term is negative ln A

Abstract

It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient.