Rotating cosmic string spacetimes are solutions to the Einstein field equations which exhibit a singularity along a timelike curve corresponding to a one dimensional source of angular momentum. These spacetimes have a notable unusual feature: they admit closed timelike curves near the so-called ``string" and are thus not globally hyperbolic. This presents challenges to studying the existence of solutions to even the linear wave equation via conventional energy methods. In current work with Jared Wunsch, we show that forward in time solutions to the wave equation (in an appropriate microlocal sense) do exist.

Our techniques involve proving a statement on propagation of singularities which provides a microlocal energy estimate that allows us to establish existence of solutions. In this talk we will discuss the dynamics of null geodesics on cosmic string spacetimes, propagation of singularities along these paths, and the utility of the resulting estimate.