Phase Space Analysis on some Black Hole Manifolds
Blue, P. · Soffer, A.
Original · EN
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 L⁶ norm in space decays like t⁻¹/³. This weight vanishes at the event horizon, but not at infinite.
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