Black hole pair creation in de Sitter space: a complete one-loop analysis

TL;DR

This paper provides a comprehensive one-loop quantum gravity analysis of black hole pair creation in de Sitter space, revealing detailed spectra, fluctuation determinants, and the impact of cosmological parameters on nucleation rates.

Contribution

It offers the first exact one-loop calculation of black hole pair creation in de Sitter space using Euclidean quantum gravity and $ ext{zeta}$-function regularization.

Findings

Black hole pairs are created at a constant volume density at late times.

The nucleation rate is strongly suppressed for small cosmological constant $ ext{Lambda}$.

The process is described as decay of a metastable thermal state in de Sitter space.

Abstract

We present an exact one-loop calculation of the tunneling process in Euclidean quantum gravity describing creation of black hole pairs in a de Sitter universe. Such processes are mediated by $S^2\times S^2$ gravitational instantons giving an imaginary contribution to the partition function. The required energy is provided by the expansion of the universe. We utilize the thermal properties of de Sitter space to describe the process as the decay of a metastable thermal state. Within the Euclidean path integral approach to gravity, we explicitly determine the spectra of the fluctuation operators, exactly calculate the one-loop fluctuation determinants in the $\zeta$-function regularization scheme, and check the agreement with the expected scaling behaviour. Our results show a constant volume density of created black holes at late times, and a very strong suppression of the nucleation rate for small values of $\Lambda$.