Generalised hyperbolicity in spacetimes with string-like singularities

TL;DR

This paper establishes well-posedness of the wave equation in spacetimes with string-like singularities, advancing the understanding of gravitational singularities as obstructions to field dynamics rather than point particles.

Contribution

It extends a framework to analyze wave equations in spacetimes with cosmic strings, linking singularities to field behavior and the Strong Cosmic Censorship Conjecture.

Findings

Wave equation well-posedness in $H^{1}$ for string-like singularities

Characterization of gravitational singularities as obstructions to test field dynamics

Implications for the Strong Cosmic Censorship Conjecture

Abstract

In this paper we present well-posedness results of the wave equation in $H^{1}$ for spacetimes that contain string-like singularities. These results extend a framework able to characterise gravitational singularities as obstruction to the dynamics of test fields rather than point particles. In particular, we discuss spacetimes with cosmic strings and the relation of our results to the Strong Cosmic Censorship Conjecture.