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).
Keywords
microstate, instability, general relativity, evanescent
ergosurface
