On the stability of black holes with nonlinear electromagnetic fields

The stability of three static and spherically symmetric black hole solutions with nonlinear electromagnetism as a source is investigated in three different ways. We show that the specific heat of all the solutions displays an infinite discontinuity with a change of sign, but the turning point method indicates that the solutions are thermodynamically stable (much in the same way as in the case of the Reissner-Nordstrom geometry). We also show that the black holes analyzed here are dynamically stable, thus suggesting that there may be a relation between thermodynamical and dynamical stability for nonvacuum black holes.