A Note On Complex Spacetime Metrics

TL;DR

This paper discusses the necessity and challenges of including complex saddle points in the gravitational path integral, proposing a speculative restriction inspired by recent work on complex metrics in quantum field theory.

Contribution

It introduces a novel speculative proposal for restricting complex saddle points in the gravitational path integral, motivated by recent theoretical developments.

Findings

Highlights the need for restrictions on complex saddle points

Proposes a new restriction based on Kontsevich and Segal's work

Connects complex metrics to topology change in quantum gravity

Abstract

For various reasons, it seems necessary to include complex saddle points in the "Euclidean" path integral of General Relativity. But some sort of restriction on the allowed complex saddle points is needed to avoid various unphysical examples. In this article, a speculative proposal is made concerning a possible restriction on the allowed saddle points in the gravitational path integral. The proposal is motivated by recent work of Kontsevich and Segal on complex metrics in quantum field theory, and earlier work of Louko and Sorkin on topology change from a real time point of view.