Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
General Relativity and Quantum Cosmology
2015-11-18 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| < M). As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave equation in any bounded-frequency regime.
Cite
@article{arxiv.1302.6902,
title = {Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime},
author = {Yakov Shlapentokh-Rothman},
journal= {arXiv preprint arXiv:1302.6902},
year = {2015}
}
Comments
Final version, to appear in Annales Henri Poincare