Lorentzian Condition in Quantum Gravity

TL;DR

This paper introduces a Lorentzian condition in quantum gravity that ensures the universe's spacetime signature and applies it to calculate black hole pair creation rates in de Sitter space, revealing non-zero semi-classical probabilities.

Contribution

It proposes a new formalism using the conjugate representation of the wave function to enforce Lorentzian signature in quantum gravity models, enabling novel calculations.

Findings

Demonstrates advantages of the formalism in nucleation of de Sitter and Nariai universes

Calculates non-zero pair creation rate for sub-maximal black holes in de Sitter space

Shows semi-classical pair creation probabilities can be non-vanishing

Abstract

The wave function of the universe is usually taken to be a functional of the three-metric on a spacelike section, Sigma, which is measured. It is sometimes better, however, to work in the conjugate representation, where the wave function depends on a quantity related to the second fundamental form of Sigma. This makes it possible to ensure that Sigma is part of a Lorentzian universe by requiring that the argument of the wave function be purely imaginary. We demonstrate the advantages of this formalism first in the well-known examples of the nucleation of a de Sitter or a Nariai universe. We then use it to calculate the pair creation rate for sub-maximal black holes in de Sitter space, which had been thought to vanish semi-classically.