Evanescent ergosurface instability

Some exotic compact objects, including supersymmetric microstate geometries and certain boson stars, possess evanescent ergosurfaces: time-like submanifolds on which a Killing vector field, which is time-like everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solutions to the linear wave equation which concentrate a finite amount of energy into an arbitrarily small spatial region, or the energy of waves measured by a stationary family of observers can be amplified by an arbitrarily large amount. In certain circumstances we can rule out the first type of instability. We also provide a generalisation to asymptotically Kaluza–Klein manifolds. This instability bears some similarity with the “ergoregion instability” of Friedman (Comm. Math. Phys. 63:3 (1978), 243–255), and we use many of the results from the recent proof of this instability by Moschidis (Comm. Math. Phys. 358:2 (2018), 437–520).