A Characterisation of Strong Wave Tails in Curved Space-Times

TL;DR

This paper characterizes when wave tails in curved space-times are strong, linking the presence of curvature-induced backscattering to the nature of the tail, with implications for electromagnetic and scalar fields in different geometries.

Contribution

It introduces a new criterion for strong wave tails based on backscattering of the radiative part of the field in curved space-times.

Findings

Electromagnetic waves in asymptotically flat space-times have weak tails.

Fields with tail-free propagation exhibit weak tails.

Scalar fields in cosmological scenarios have strong tails.

Abstract

A characterisation of when wave tails are strong is proposed. The existence of a curvature induced tail (i.e. a Green's function term whose support includes the interior of the light-cone) is commonly understood to cause backscattering of the field governed by the relevant wave equation. Strong tails are characterised as those for which the purely radiative part of the field is backscattered. With this definition, it is shown that electromagnetic waves in asymptotically flat space-times and fields governed by tail-free propagation have weak tails, but minimally coupled scalar fields in a cosmological scenario have strong tails.