On the thermodynamical stability of black holes in nonlinear electrodynamics

We analyze the thermodynamical stability of static and spherically symmetric black hole solutions with nonlinear electromagnetism as a source, and show that any sequence of such black holes in isolation that includes the Schwarzschild black hole is stable in the (βM,M)(βM,M) plane for any nonlinear Lagrangian describing the electromagnetic field. The study of three exact solutions (which include the Schwarzschild solution in some limit) in the (βQ,Q)(βQ,Q) plane show that they are stable in the microcanonical ensemble, and unstable or less unstable (due to the existence of a turning point) in the canonical ensemble. If the less unstable configurations are stable, our results indicate that they would be in equilibrium with a reservoir at a higher temperature than the corresponding Reissner–Nordstrom configuration. An expression for the heat capacity at constant charge valid for any Lagrangian describing nonlinear electromagnetism is also presented. It displays a divergence with a change of sign that occurs precisely at the turning point obtained by the Poincarè method.