Price's Law on Nonstationary Spacetimes
Abstract
In this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t-3 local uniform decay rate (Price's law MR0376103) for linear waves. As a corollary, we also prove Price's law for certain small perturbations of the Kerr metric. This result was previously established by the second author in Tat on stationary backgrounds. The present work was motivated by the problem of nonlinear stability of the Kerr/Schwarzschild solutions for the vacuum Einstein equations, which seems to require a more robust approach to proving linear decay estimates.