Microcanonical description of (micro) black holes

TL;DR

This paper advocates for using the microcanonical ensemble to describe black holes, providing a consistent framework that overcomes issues of negative specific heat and unitarity loss present in traditional thermodynamic models, especially relevant for micro-black holes.

Contribution

It introduces a microcanonical approach to black hole thermodynamics, addressing limitations of the canonical ensemble and applicable across all energy scales, including micro-black holes.

Findings

Microcanonical ensemble resolves negative specific heat issues.

Provides a consistent description of Hawking radiation.

Applicable to micro-black holes in extra-dimensional models.

Abstract

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g. negative specific heat and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existence is predicted in models with extra- spatial dimensions.