  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.
