Phase Space Analysis on some Black Hole Manifolds

Details Phase Space Analysis on some Black Hole Manifolds Phase Space Analysis on some Black Hole Manifolds

2005-11-10

arxiv.org/abs/math/0511281v2

Mathematics

Analysis of PDEs

63 pages (correction to Morawetz multiplier- 14 August 2006)

Scientific paper

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.

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