Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 6

The wave equation in a general spherically symmetric black hole geometry

Pages: 1789 – 1815



Matthew Masarik (SRI International, Ann Arbor, Mich.)


We consider the Cauchy problem for the wave equation in ageneral class of spherically symmetric black holegeometries. Under certain mildconditions on the far-field decay and the singularity, weshow that there is a unique globally smooth solution to theCauchy problem for the wave equation with data compactlysupported away from the horizon that is compactly supportedfor all times and \emph{decays in $L^{\infty}_{\text{loc}}$as $t$ tends to infinity}. We obtain as a corollary that inthe geometry of black hole solutions of the SU(2)Einstein/Yang--Mills equations, solutions to the waveequation with compactly supported initial data decay as $t$goes to infinity.

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