Exact nonsingular black holes and thermodynamics

We show that regular black holes given by Culetu [14]can be obtained by coupling Einstein's gravity with the nonlinear electrodynamics source. The non-singular black hole has a mass function m(r) =Me^−k/r, k is the deviation parameter, and it interpolates between the Schwarzschild black hole (k=0) and the Reissner-Nordstrom black hole (r>>k). Interestingly, there exists a critical mass parameter M=M^c, which corresponds to an extremal black hole when Cauchy and event horizons coincide. For M>M^c, it describes a nonextremal black hole with two horizons and no black hole for Mc. The Hawking temperature of the nonsingular black hole is maximum, where the specific heat diverges and changes its sign at the value of mass M_c2>M_c1, and the second-order phase transition occurs at that point. The smaller nonsingular black holes are always stable due to positive heat capacity and negative free energy. A discussion on the quasinormal modes of scalar field perturbations on nonsingular black holes background is included. (author)