Decay for wave equation solutions on Schwarzschild backgrounds

Abstract

In this paper we present a new approach to proving the integrated local energy decay (ILED) in the context of the proof of pointwise and energy decay for solutions to the wave equation on black hole backgrounds. The approach uses commutation with angular momentum Killing vector fields to take advantage of the harmonic decomposition of a wave equation solution. We work in the Schwarzschild spacetime, with explicit constructions for the required vector field multipliers.