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December 2011 The wave equation in a general spherically symmetric black hole geometry
Matthew Masarik
Adv. Theor. Math. Phys. 15(6): 1789-1815 (December 2011).

Abstract

We consider the Cauchy problem for the wave equation in a general class of spherically symmetric black hole geometries. Under certain mild conditions on the far-field decay and the singularity, we show that there is a unique globally smooth solution to the Cauchy problem for the wave equation with data compactly supported away from the horizon that is compactly supported for all times and decays in $L_{loc}^\infty$ as $t$ tends to infinity. We obtain as a corollary that in the geometry of black hole solutions of the SU(2) Einstein/Yang–Mills equations, solutions to the wave equation with compactly supported initial data decay as $t$ goes to infinity.

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Matthew Masarik. "The wave equation in a general spherically symmetric black hole geometry." Adv. Theor. Math. Phys. 15 (6) 1789 - 1815, December 2011.

Information

Published: December 2011
First available in Project Euclid: 12 December 2012

zbMATH: 1261.83020
MathSciNet: MR2989813

Rights: Copyright © 2011 International Press of Boston

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Vol.15 • No. 6 • December 2011
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