An Analysis of Wave Tails based on the Geometric Optics Approximation

TL;DR

This paper investigates how wave tails affect scalar wave propagation in curved space-time using geometric optics approximation, revealing conditions under which tails influence wave behavior and when the approximation fails.

Contribution

It formulates the geometric optics approximation in terms of flux integrals and analyzes its validity across different space-times, highlighting tail effects and breakdown scenarios.

Findings

Waves in Minkowski space-time are tail-free.

Weak tails are present in Schwarzschild space-time.

Strong tails in cosmology can cause the approximation to break down.

Abstract

The effect of the existence of tails on the propagation of scalar waves in curved space-time is considered via an analysis of flux integrals of the energy-stress-momentum tensor of the waves. The geometric optics approximation is formulated in terms of such flux integrals, and three examples are investigated in detail in order to determine the possible effects of wave tails. The approximation is valid for waves in Minkowski space-time (tail-free) and waves in Schwarzschild space-time (weak tails) but it is shown how the approximation can break down in a cosmological scenario due to destructive interference by strong tails. In this last situation, the waves do not radiate.