2011/06/21 by Masarik, Matthew P.
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1106.4225
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 \emphdecays in L∞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.