Exact nonsingular black holes and thermodynamics

Abstract

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=Mc, which corresponds to an extremal black hole when Cauchy and event horizons coincide. For M>Mc, it describes a nonextremal black hole with two horizons and no black hole for M<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 Mc2>Mc1, 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.