## Advances in Theoretical and Mathematical Physics

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1355321972

**Mathematical Reviews number (MathSciNet)**

MR2989813

**Zentralblatt MATH identifier**

1261.83020

#### Citation

Masarik, Matthew. The wave equation in a general spherically symmetric black hole geometry. Adv. Theor. Math. Phys. 15 (2011), no. 6, 1789--1815. https://projecteuclid.org/euclid.atmp/1355321972