Wave Tails in Time Dependent Backgrounds

TL;DR

This paper investigates how the late-time behavior of spherical waves is affected by time-dependent scattering potentials, revealing modifications to tail structures through analytical and numerical methods.

Contribution

It introduces an analysis of wave tails in time-dependent backgrounds, extending previous studies limited to static potentials.

Findings

Tail structures are altered by the temporal variation of the potential.

Analytical predictions are validated by numerical simulations.

Time dependence leads to new features in wave decay patterns.

Abstract

It is well-known that waves propagating under the influence of a scattering potential develop ``tails''. However, the study of late-time tails has so far been restricted to time-independent backgrounds. In this paper we explore the late-time evolution of spherical waves propagating under the influence of a {\it time-dependent} scattering potential. It is shown that the tail structure is modified due to the temporal dependence of the potential. The analytical results are confirmed by numerical calculations.