Resolvent estimates for spacetimes bounded by Killing horizons
Analysis of PDEs
2018-10-10 v3 General Relativity and Quantum Cosmology
Spectral Theory
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.
Cite
@article{arxiv.1705.04251,
title = {Resolvent estimates for spacetimes bounded by Killing horizons},
author = {Oran Gannot},
journal= {arXiv preprint arXiv:1705.04251},
year = {2018}
}
Comments
27 pages. Contains some improved results. To appear in Anal. PDE