Universes inside a Lambda black hole

We address the question of universes inside a Lambda black hole which is de scribed by a spherically symmetric globally regular solution to the Einstei n equations with a variable cosmological term A(mu nu), asymptotically Ag-m u nu as r --> 0 with Lambda of the scale of symmetry restoration. Global st ructure of spacetime contains an infinite sequence of black and white holes , vacuum regular cores and asymptotically hat universes. Regular core of a A white hole models the initial stages of the Universe evolution. In this m odel it starts from a nonsingular nonsimultaneous big bang, which is follow ed 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 e stimate also the probability of quantum birth of baby universes inside a A black hole due to quantum instability of the de Sitter vacuum. (C) 2001 Els evier Science B.V. All rights reserved.