From Euclidean to Lorentzian General Relativity: The Real Way

TL;DR

This paper introduces a novel 'real Wick rotation' method to connect Riemannian and Lorentzian solutions in general relativity, providing a flexible formalism for signature change and related problems.

Contribution

It proposes a modified action with two real parameters to control spacetime signature, enabling new insights into signature change and quantum gravity issues.

Findings

Applied the method to Schwarzschild metric

Demonstrated control over solution signatures

Discussed implications for black hole thermodynamics

Abstract

We study in this paper a new approach to the problem of relating solutions to the Einstein field equations with Riemannian and Lorentzian signatures. The procedure can be thought of as a "real Wick rotation". We give a modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations. We show how this procedure works for the Schwarzschild metric and discuss some possible applications of the formalism in the context of signature change, the problem of time, black hole thermodynamics...