Instability results for the wave equation in the interior of Kerr black holes

Author: 

Luk, J
Sbierski, J

Publication Date: 

1 October 2016

Journal: 

Journal of Functional Analysis

Last Updated: 

2021-06-20T02:37:45.88+01:00

Issue: 

7

Volume: 

271

DOI: 

10.1016/j.jfa.2016.06.013

page: 

1948-1995

abstract: 

© 2016 Elsevier Inc. We prove that a large class of smooth solutions ψ to the linear wave equation □ g ψ=0 on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More precisely, we show that assuming appropriate upper and lower bounds on the energy along the event horizon, the solution has infinite (non-degenerate) energy on any spacelike hypersurfaces intersecting the Cauchy horizon transversally. Extrapolating from known results in the Reissner–Nordström case, the assumed upper and lower bounds required for our theorem are conjectured to hold for solutions arising from generic smooth and compactly supported initial data on a Cauchy hypersurface. This result is motivated by the strong cosmic censorship conjecture in general relativity.

Symplectic id: 

819443

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article