Universes inside a $\Lambda$ black hole

Abstract

We address the question of universes inside a $\Lambda$ black hole which is described by a spherically symmetric globally regular solution to the Einstein equations with a variable cosmological term ${\Lambda }_{\mu \nu }$, asymptotically $\Lambda g_{\mu \nu }$ as $r\to 0$ with $\Lambda$ 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 $\Lambda$ 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 $\Lambda$ black hole due to quantum instability of the de Sitter vacuum.

REVTEX, 9 pages, 13 figures. To appear in Physics Letters B

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