Time kink: modeling change of metric signature

TL;DR

This paper models a continuous change in spacetime metric signature from Lorentzian to Euclidean using a time-dependent kink, solving Einstein equations and exploring implications like inflation without extra fields.

Contribution

It introduces a new model for signature change with a time-dependent kink in the metric and analyzes Einstein equations and junction conditions across the hypersurface.

Findings

Demonstrates inflation as a consequence of signature change

Constructs a metric describing continuous signature transition

Analyzes Einstein tensor discontinuities and junction conditions

Abstract

The model of a signature change of a metric from the Lorenztian to Euclidean one with the use of a time dependent kink as $g_{00}$ component of the metric is considered. The metric which describes the continuous change of the signature of this type on a hypersurface is constructed and corresponding Einstein equations are solved in both regions of the space-time. The discontinuities of the Einstein tensor components on the hypersurface are discussed as well as junction conditions for the parameters of the solutions. Additionally, the properties of a transition from the space-time with one signature to an another are discussed, the presence of an inflation in the model is demonstrated as a consequence of the signature change without any additional fields required.