Black holes, cosmological singularities and change of signature

TL;DR

The paper argues that changing spacetime signature cannot prevent singularities unless Einstein's equations are modified at the signature change surface, and explores the initial value problem for such solutions.

Contribution

It demonstrates the necessity of abandoning Einstein's equations at signature change surfaces to avoid singularities and compares smooth versus discontinuous signature change solutions.

Findings

Signature change alone cannot avoid singularities without modifying Einstein's equations.

Smooth and discontinuous solutions to signature change are largely equivalent.

Provides insights into the initial value problem for signature-changing spacetimes.

Abstract

There exists a widespread belief that signature type change could be used to avoid spacetime singularities. We show that signature change cannot be utilised to this end unless the Einstein equation is abandoned at the suface of signature type change. We also discuss how to solve the initial value problem and show to which extent smooth and discontinuous signature changing solutions are equivalent.