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 so-called "string". This presents challenges to studying the existence of solutions to the wave equation via conventional energy methods. In this work, we show that forward solutions to the wave equation (in an appropriate microlocal sense) do exist. Our techniques involve proving a statement on propagation of singularities and using the resulting estimates to show existence of solutions. This is joint work with Jared Wunsch.
Wave propagation on rotating cosmic string spacetimes
Katrina Morgan, Temple UniversityAuthors: Katrina Morgan and Jared Wunsch
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]