Universes inside a $\Lambda$ black hole

TL;DR

This paper explores a spherically symmetric solution to Einstein's equations with a variable cosmological term, proposing a model where black holes contain nested universes, including a nonsingular big bang and potential quantum baby universes.

Contribution

It introduces a novel regular black hole solution with a variable cosmological term, modeling universe creation inside black holes and analyzing quantum birth probabilities.

Findings

Spacetime contains infinite black and white holes with regular cores.

The regular core models the universe's initial nonsingular big bang.

Quantum instability of de Sitter vacuum suggests possible baby universe creation.

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.