Resolvent estimates for spacetimes bounded by Killing horizons

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 non-degenerate 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.

27 pages. Contains some improved results. To appear in Anal. PDE

References in corpus (2)

• On quasinormal modes of asymptotically anti-de Sitter black holes
• Global uniqueness theorems for linear and nonlinear waves

Cited by in corpus (1)

• Semiclassical Estimates for Scattering on the Real Line