Resolvent estimates for spacetimes bounded by Killing Horizons

Oran Gannot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)537-560
Number of pages24
JournalAnalysis and PDE
Volume12
Issue number2
DOIs
StatePublished - 2018

Keywords

  • Carleman estimates
  • Killing horizons
  • Logarithmic decay
  • Resolvent bounds

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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