Vol. 12, No. 2, 2019

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Resolvent estimates for spacetimes bounded by Killing horizons

Oran Gannot

Vol. 12 (2019), No. 2, 537–560
DOI: 10.2140/apde.2019.12.537
Abstract

We show that the resolvent grows at most exponentially with frequency for the wave equation on a class of stationary spacetimes which are bounded by nondegenerate Killing horizons, without any assumptions on the trapped set. Correspondingly, there exists an exponentially small resonance-free region, and solutions of the Cauchy problem exhibit logarithmic energy decay.

Keywords
logarithmic decay, resolvent bounds, Killing horizons, Carleman estimates
Mathematical Subject Classification 2010
Primary: 35L05, 35P25, 35R01, 83C57
Milestones
Received: 20 February 2018
Revised: 27 April 2018
Accepted: 30 May 2018
Published: 14 August 2018
Authors
Oran Gannot
Department of Mathematics
Northwestern University
Evanston, IL
United States