Can Black Hole be Created at the Birth of the Universe?

TL;DR

This paper investigates the quantum creation of black hole pairs in (anti-)de Sitter space, linking their formation probabilities to the universe's entropy and black hole horizon areas, providing insights into early universe conditions.

Contribution

It introduces a method to compute black hole pair creation probabilities from constrained instantons, relating them to entropy and horizon areas in various cosmological backgrounds.

Findings

Creation probability for chargeless, nonrotating black holes equals exponential of negative universe entropy.

For other cases, creation probability relates to the sum of black hole horizon areas.

Method applies to both closed and open universe models without a general no-boundary proposal.

Abstract

We study the quantum creation of black hole pairs in the (anti-)de Sitter space background. These black hole pairs in the Kerr-Newman family are created from constrained instantons. At the $WKB$ level, for the chargeless and nonrotating case, the relative creation probability is the exponential of (the negative of) the entropy of the universe. Also for the remaining cases of the family, the creation probability is the exponential of (the negative of) one quarter of the sum of the inner and outer black hole horizon areas. In the absence of a general no-boundary proposal for open universes, we treat the creations of the closed and the open universes in the same way.