## Advances in Theoretical and Mathematical Physics

### The wave equation in a general spherically symmetric black hole geometry

Matthew Masarik

#### 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.

#### Article information

Source
Adv. Theor. Math. Phys., Volume 15, Number 6 (2011), 1789-1815.

Dates
First available in Project Euclid: 12 December 2012