The Wave Equation in a General Spherically Symmetric Black Hole Geometry

Details The Wave Equation in a General Spherically Symmetric Black Hole Geometry The Wave Equation in a General Spherically Symmetric Black Hole Geometry

2011-06-21

arxiv.org/abs/1106.4225v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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Scientific paper

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 \emph{decays in $L^{\infty}_{\text{loc}}$ 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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