Anomalously small wave tails in higher dimensions

Abstract

We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Along the way we clarify and amend some confounding arguments and statements in the literature of the subject.