Resolvent estimates for spacetimes bounded by Killing horizons

Gannot, Oran

doi:10.2140/apde.2019.12.537

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

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

Vol. 12, No. 2, 2019