Black-and-white hole as a space-time with integrable singularity

Abstract

We discuss the problem of singularities in general relativity and emphasize the distinction that should be made between what is understood to be mathematical and physical singularities. We revise examples of space-times that conventionally contain a singularity which, in a sense, does not manifest itself physically. A special attention is paid to the case of integrable singularities for which we propose a well-defined mathematical procedure used to extend the space-time beyond the singularity. We argue that this type of singularity may connect the interior of a black hole with a newly born universe (a space-time referred to as black-and-white hole) giving a resolution to the problem of initial high density and symmetry of the universe. We exemplify by presenting toy models of eternal and astrophysical black-and-white holes.