A little hair can make a big difference: thermodynamic stability of quasi-bald asymptotically-flat black holes

TL;DR

This paper investigates the thermodynamic stability of asymptotically-flat hairy black holes, revealing that even nearly bald black holes can be thermodynamically unstable despite their dynamical and entropic preferences.

Contribution

It demonstrates that certain quasi-bald black holes are thermodynamically unstable in the canonical ensemble, challenging assumptions about stability based on hair presence.

Findings

Quasi-bald black holes are thermodynamically unstable for all global charges.

Hair does not guarantee thermodynamic stability in the models studied.

Stable phases can be dynamically and entropically preferred yet thermodynamically unstable.

Abstract

The local thermodynamic stability of a black hole (BH) in the canonical ensemble is defined by the positivity of the specific heat at constant global charges. Schwarzschild BHs in thermodynamic equilibrium with an energy reservoir are always unstable against small fluctuations of energy, whereas sufficiently near-extremal Reissner-Nordstr\"{o}m/Kerr BHs are stable. One could expect that asymptotically-flat hairy BHs branching off from such stable phases would also be, by continuity, locally thermodynamically stable for vanishingly little hair. We show this is not the case in some models, including scalarized BHs bifurcating from Reissner-Nordstr\"{o}m and spinning BHs with synchronized hair bifurcating from Kerr. Specifically, it is found that quasi-bald BHs are locally thermodynamically unstable in the canonical ensemble for all global charges and regardless of being dynamically and entropically preferred over bald ones at fixed global charges.