Evanescent ergosurface instability
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.
Cite
@article{arxiv.1810.03026,
title = {Evanescent ergosurface instability},
author = {Joseph Keir},
journal= {arXiv preprint arXiv:1810.03026},
year = {2020}
}
Comments
Final version, accepted for publication in APDE. Typos corrected, a new argument is presented in section 11 correcting the original argument. This new argument proceeds via a double interpolation argument, making use of a time and angular frequency decomposition. 71 pages, 3 figures