The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms

Abstract

In this paper, we present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation [Formula: see text] on the exterior of the Schwarzschild geometry [Formula: see text]. Here [Formula: see text] is a regular vector field on [Formula: see text] decaying suitably in space but not necessarily in time. The proof is formulated to cover also perturbations of the Regge–Wheeler equation.