The wave equation on singular space-times

TL;DR

This paper establishes the local unique solvability of the wave equation on a broad class of weakly singular, locally bounded space-time metrics using generalized functions, advancing the understanding of wave behavior in singular geometries.

Contribution

It introduces a method to prove local unique solvability of the wave equation on weakly singular space-times within a generalized functions framework.

Findings

Proved local unique solvability for a large class of singular metrics.

Extended the applicability of wave equation solutions to singular space-times.

Utilized generalized functions to handle weak singularities.

Abstract

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.