Quantum Creation of a Black Hole

TL;DR

This paper explores the quantum creation of black holes in the early universe using the Hartle-Hawking no-boundary proposal, linking black hole probability to horizon areas and entropy.

Contribution

It introduces a method to calculate the probability of black hole creation at universe's birth via gravitational instantons with conical singularities.

Findings

Black hole creation probability is exponential of quarter the sum of horizon areas.

The total entropy of the universe relates directly to black hole and cosmological horizons.

The approach applies to all black holes in de Sitter space background.

Abstract

Using the Hartle-Hawking no-boundary proposal for the wave function of the universe, we can study the wave function and probability of a single black hole created at the birth of the universe. The black hole originates from a constrained gravitational instanton with conical singularities. The wave function and probability of a universe with a black hole are calculated at the $WKB$ level. The probability of a black hole creation is the exponential of one quarter of the sum of areas of the black hole and cosmological horizons. One quarter of this sum is the total entropy of the universe. We show that these arguments apply to all kinds of black holes in the de Sitter space background.