Solutions to the wave equation describe phenomena like propagation of light and sound waves. The most basic form of this equation is well studied and well understood. Explicit solutions can be found e.g. via Fourier methods. The picture gets more complicated in different scenarios like waves moving through inhomogeneous media or on geometric backgrounds arising in general relativity. Energy methods have historically been a useful tool for studying such variations of the wave equation. Under the right conditions, solutions to the wave equation satisfy energy estimates which state that the energy of the solution $u$ at time $t$ is controlled by the energy of the initial data. However, such techniques are not always available, which is the case for waves on rotating cosmic string spacetimes. These geometries are solutions to the Einstein field equations which exhibit a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. They have a notable unusual feature: they admit closed timelike curves near the so-called ``string". In joint work with Jared Wunsch, we show that \textit{forward in time} solutions to the wave equation (in an appropriate microlocal sense) do exist on rotating cosmic string spacetimes, despite the causality issues present in the geometry. Our techniques involve proving a statement on propagation of singularities which provides a microlocal version of an energy estimate that allows us to establish existence of solutions.