Light-like Signals in General relativity and Cosmology

TL;DR

This paper investigates light-like signals such as impulsive gravitational waves and shells in General Relativity, analyzing their geometric properties, interactions with matter, and illustrating their behavior in various cosmological and space-time models.

Contribution

It provides a systematic analysis of light-like signals using Penrose's classification, including their interactions with matter and applications to different space-time geometries.

Findings

Derived geometric conditions for light-like signals.

Analyzed interactions with cosmic fluids.

Presented examples in cosmological and vacuum space-times.

Abstract

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.