Anomalously small wave tails in higher dimensions

TL;DR

This paper investigates late-time wave tails in higher even-dimensional Minkowski spacetime, revealing special potentials that cause anomalously small and rapidly decaying tails, and clarifies previous misconceptions in the literature.

Contribution

It identifies exceptional potentials in six and higher even dimensions that produce anomalously small wave tails, advancing understanding of wave decay in higher-dimensional spacetimes.

Findings

Existence of exceptional potentials in six and higher even dimensions

Wave tails can have anomalously small amplitudes

Wave decay can be faster than previously thought

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.