Generalised hyperbolicity in conical space-times

TL;DR

This paper investigates wave equations in conical space-times with cosmic strings using Colombeau algebras, establishing existence, uniqueness, and a new concept of generalised hyperbolicity for such singular geometries.

Contribution

It introduces a framework for analyzing wave equations in singular space-times via Colombeau algebras, proving G-hyperbolicity for conical geometries.

Findings

Existence and uniqueness of wave solutions in Colombeau algebra G.

Solutions are associated with distributional solutions.

Conical space-times are shown to be G-hyperbolic.

Abstract

Solutions of the wave equation in a space-time containing a thin cosmic string are examined in the context of non-linear generalised functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra G is established for a conical space-time and this solution is shown to be associated to a distributional solution. A concept of generalised hyperbolicity, based on test fields, can be defined for such singular space-times and it is shown that a conical space-time is G-hyperbolic.