Generalised hyperbolicity in space-times with conical singularities

TL;DR

This paper demonstrates that space-times with conical singularities, modeling cosmic strings, are hyperbolic by establishing the existence of unique solutions to the wave equation initial value problem.

Contribution

It proves hyperbolicity for space-times with conical singularities, extending the understanding of wave equations in such singular geometries.

Findings

Unique H^1 solutions exist for the wave equation in conical space-times.

Space-times with cosmic string singularities are hyperbolic.

The results support the well-posedness of wave propagation in these geometries.

Abstract

It is shown that the space-time with a conical singularity, which describes a thin cosmic string, is hyperbolic in the sense that a unique H^1 solution exists to the initial value problem for the wave equation with a certain class of initial data.