On Thermal Stability of Hairy Black Holes

TL;DR

This paper investigates the thermodynamical stability of hairy black holes with secondary scalar hair, deriving conditions for stability and exploring implications for quantum spacetime minimum length.

Contribution

It provides a model-independent analysis of the stability conditions for hairy black holes considering backreaction effects and scalar hair induced by quadratic-curvature interactions.

Findings

Stable configurations involve extremal black holes with inner horizons.

Thermal stability depends on the scalar hair and geometry modifications.

Implications for minimum length in quantum spacetime are discussed.

Abstract

We discuss thermodynamical stability for hairy black hole spacetimes, viewed as defects in the thermodynamical parameter space, taking into account the backreaction of a secondary hair onto the spacetime geometry, which is modified non trivially. We derive, in a model independent way, the conditions for the hairy black hole with the secondary hair to reach a stable thermal equilibrium with the heat bath. Specifically, if the scalar hair, induced by interactions of the matter fields with quadratic-curvature corrections, produces an inner horizon in the deformed geometry, a thermodynamically stable configuration will be reached with the black hole becoming extremal in its final stage. We also attempt to make some conjectures concerning the implications of this thermal stability for the existence of a minimum length in a quantum space time.