# Thermal stability of black holes with arbitrary hairs

## TL;DR

This paper develops a generalized criterion for the thermal stability of black holes with arbitrary hairs using loop quantum gravity and statistical mechanics, predicting stability or instability under Hawking radiation.

## Contribution

It extends previous stability criteria to black holes with arbitrary hairs without relying on classical spacetime geometry, using quantum gravity and thermodynamics.

## Key findings

- Derived stability criteria applicable to black holes with arbitrary hairs.
- Identified conditions under which black holes are thermally unstable.
- Validated criteria against specific black hole solutions.

## Abstract

We have derived the criteria for thermal stability of charged rotating black holes, for horizon areas that are large relative to the Planck area (in these dimensions). In this paper, we generalized it for black holes with arbitrary hairs. The derivation uses results of loop quantum gravity and equilibrium statistical mechanics of the grand canonical ensemble and there is no explicit use of classical spacetime geometry at all in this analysis. The assumption is that the mass of the black hole is a function of its horizon area and all the hairs. Our stability criteria are then tested in detail against some specific black holes, whose metrics provide us with explicit relations for the dependence of the mass on the area and other hairs of the black holes. This enables us to predict which of these black holes are expected to be thermally unstable under Hawking radiation.