Detection of Impulsive Light-Like Signals in General Relativity

TL;DR

This paper investigates how impulsive light-like signals, composed of null matter shells and gravitational waves, affect neighboring test particles, revealing displacement and distortion effects depending on the shell's stress properties.

Contribution

It provides a detailed analysis of test particle responses to impulsive light-like signals, including effects of anisotropic stress and gravitational waves, with explicit examples.

Findings

Anisotropic stress causes test particles to displace out of the signal front.

No anisotropic stress results in reduced gravitational wave distortion.

Explicit example demonstrates effects in plane-fronted signals.

Abstract

The principal purpose of this paper is to study the effect of an impulsive light-like signal on neighbouring test particles. Such a signal can in general be unambiguously decomposed into a light-like shell of null matter and an impulsive gravitational wave. Our results are: (a) If there is anisotropic stress in the light-like shell then test particles initially moving in the signal front are displaced out of this 2-surface after encountering the signal; (b) For a light-like shell with no anisotropic stress accompanying a gravitational wave the effect of the signal on test particles moving in the signal front is to displace them relative to each other with the usual distortion due to the gravitational wave diminished by the presence of the light-like shell. An explicit example for a plane-fronted signal is worked out.