Evanescent ergosurface instability

TL;DR

The paper demonstrates a linear instability in manifolds with evanescent ergosurfaces lacking an event horizon, showing potential energy concentration or amplification of waves, with implications for exotic compact objects.

Contribution

It introduces a new type of linear instability for manifolds with evanescent ergosurfaces, extending the understanding of ergoregion instabilities to these geometries.

Findings

Existence of solutions concentrating energy in small regions.

Possibility of arbitrarily large wave energy amplification.

Generalization to asymptotically Kaluza-Klein manifolds.

Abstract

Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike 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, and we use many of the results from the recent proof of this instability by Moschidis.