Mode solutions to the wave equation on a rotating cosmic string background

TL;DR

This paper develops microlocal techniques to construct solutions for wave and Klein-Gordon equations on a rotating cosmic string background, overcoming challenges posed by singularities and lack of global hyperbolicity.

Contribution

It introduces a novel microlocal approach to solve wave equations on singular, non-globally hyperbolic spacetimes like rotating cosmic strings, focusing on single angular modes.

Findings

Constructed forward parametrices for wave and Klein-Gordon equations

Addressed singularities along the timelike line

Extended solution methods to non-globally hyperbolic backgrounds

Abstract

A static rotating cosmic string metric is singular along a timelike line and fails to be globally hyperbolic; these features make it difficult to solve the wave equation by conventional energy methods. Working on a single angular mode at a time, we use microlocal methods to construct forward parametrices for wave and Klein--Gordon equations on such backgrounds.