Paper
A note on energy currents and decay for the wave equation on a Schwarzschild background
Authors
Mihalis Dafermos, Igor Rodnianski
Abstract
In recent work, we have proven uniform decay bounds for solutions of the wave equation on a Schwarzschild exterior, in particular, the uniform pointwise estimate , which holds throughout the domain of outer communications, where is an advanced Eddington-Finkelstein coordinate, , and is a constant depending on a Sobolev norm of initial data. A crucial estimate in the proof required a decomposition into spherical harmonics. We here give an alternative proof of this estimate not requiring such a decomposition.