Physical Properties of a Regular Rotating Black Hole: Thermodynamics, Stability, Quasinormal Modes.

Respecting the angular momentum conservation of torque-free systems, it is natural to consider rotating solutions of massive objects. Besides that, motivated by the realistic astrophysical black holes that rotate, we use the Newman-Janis formalism to construct a regular rotating black hole. We start with a nonlinearly charged regular static black hole in the framework of the standard general relativity and then obtain the associated rotating solution through such a formalism. We investigate the geometrical properties of the metric by studying the boundary of ergosphere. We also analyze thermodynamic properties of the solution in AdS spacetime and examine thermal stability and possible phase transition. In addition, we perturb the black hole by using of a real massless scalar field as a probe to investigate its dynamic stability. We obtain an analytic expression for the real and imaginary parts of the quasinormal frequencies. Finally, we look for a connection between the quasinormal frequencies and the properties of the photon sphere in the eikonal limit.