Wave propagation on rotating cosmic string spacetimes

TL;DR

This paper demonstrates the existence of semi-global solutions to the wave equation on rotating cosmic string spacetimes, despite their non-globally hyperbolic nature and presence of closed timelike curves, using microlocal analysis and propagation of singularities.

Contribution

It introduces a novel microlocal approach to establish semi-global wave solutions in non-globally hyperbolic spacetimes with singularities and closed timelike curves.

Findings

Existence of semi-global wave solutions in rotating cosmic string spacetimes.

Propagation of singularities relates energy entering and leaving the string.

Solutions are localized microlocally but global in time.

Abstract

A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This presents challenges to studying the existence of solutions to the wave equation via conventional energy methods. In this work, we show that semi-global forward solutions to the wave equation do nonetheless exist, but only in a microlocal sense. The main ingredient in this existence theorem is a propagation of singularities theorem that relates energy entering the string to energy leaving the string. The propagation theorem is localized in the fibers of a certain fibration of the blown-up string, but global in time, which means that energy entering the string at one time may emerge previously.