Regular Rotating Black Holes and Solitons

Abstract

Solutions describing regular rotating black holes are typically obtained by applying the Newman-Janis complex translation to spherical metrics of the Kerr-Schild class. Regular solutions of this class are specified by T_t^t = T_r^r and have necessarily de Sitter centers provided that the source terms T_kⁱ satisfy the weak energy condition. Rotation transforms a de Sitter center into a de Sitter vacuum disk which is the generic common constituent of all regular rotating objects. In nonlinear electrodynamics coupled to gravity all metrics belong to the Kerr-Schild class and have the Kerr-Newman asymptotic for a distant observer. The ring singularity is replaced with the superconducting ring current which represents an electromagnetic nondissipative source of any asymptotically Kerr-Newman geometry. We outline the basic generic features of regular rotating black holes and solitons which are regular compact objects without event horizons, replacing naked singularities.