Quasi-normal Modes of Topological Stars

We study the quasi-normal mode spectrum of topological stars which have the same asymptotic properties as black holes. These are coherent states in string theory corresponding to pure deformations of spacetime through the dynamics of compact extra dimensions. The topological stars are classified as either "first" or "second" kind, based on the presence of either one or two light rings, respectively. The quasi-normal mode spectrum is analytically computed using a WKB analysis, and compared with a numerically generated spectrum using Leaver's method. We discuss the connection between the quasi-normal modes and the physics of the unstable light-rings, in both cases of the "first" and "second" kind of topological star. We find good agreement with numerical and analytic results, comparable to the WKB level agreement in Schwarzschild black holes.