Vol. 13, No. 6, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 7, 1955–2257
Issue 6, 1605–1954
Issue 5, 1269–1603
Issue 4, 945–1268
Issue 3, 627–944
Issue 2, 317–625
Issue 1, 1–316

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Evanescent ergosurface instability

Joe Keir

Vol. 13 (2020), No. 6, 1833–1896
Abstract

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
Mathematical Subject Classification 2010
Primary: 35L05, 35Q75, 58J45, 83C57
Secondary: 83E50
Milestones
Received: 19 October 2018
Revised: 13 June 2019
Accepted: 13 August 2019
Published: 12 September 2020
Authors
Joe Keir
Department of Applied Mathematics and Theoretical Physics
Centre for Mathematical Sciences
University of Cambridge
Cambridge
United Kingdom