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Phase Space Analysis on some Black Hole Manifolds

Research paper by P. Blue, A. Soffer

Indexed on: 14 Aug '06Published on: 14 Aug '06Published in: Mathematics - Analysis of PDEs



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.