Thermodynamic stability of quasibald asymptotically flat black holes

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-Nordström/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-Nordström and spinning BHs with synchronized hair bifurcating from Kerr. Specifically, it is found that quasibald 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