Universes inside a $Λ$ black hole

Abstract

We address the question of universes inside a $Λ$ black hole which is described by a spherically symmetric globally regular solution to the Einstein equations with a variable cosmological term $Λ_{μν}$, asymptotically $Λg_{μν}$ as $r\to 0$ with $Λ$ of the scale of symmetry restoration. Global structure of spacetime contains an infinite sequence of black and white holes, vacuum regular cores and asymptotically flat universes. Regular core of a $Λ$ white hole models the initial stages of the Universe evolution. In this model it starts from a nonsingular nonsimultaneous big bang, which is followed by a Kasner-type anisotropic expansion. Creation of a mass occurs mostly at the anisotropic stage of quick decay of the initial vacuum energy. We estimate also the probability of quantum birth of baby universes inside a $Λ$ black hole due to quantum instability of the de Sitter vacuum.