Phase Space Analysis on some Black Hole Manifolds
arXiv:math/0511281 · doi:10.1016/j.jfa.2008.10.004
Abstract
The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space- times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space- time of this type. We show that for solutions with initial data which decay at infinite, a weighted $L^6$ norm in space decays like $t^{-1/3}$. This weight vanishes at the event horizon, but not at infinite.
63 pages (correction to Morawetz multiplier- 14 August 2006)