Interpreting a conformally flat pure radiation space-time

TL;DR

This paper provides a physical interpretation of conformally flat pure radiation space-times, analyzing their wave surfaces, impulsive limits, and global structure, including potential vacuum extensions.

Contribution

It offers a novel physical interpretation of a class of conformally flat pure radiation metrics and explores their global structure and wave surface behavior.

Findings

Wave surfaces can be represented as null hyperplanes in the weak field limit.

In the impulsive limit, solutions reduce to pp-waves with propagation direction depending on retarded time.

A coordinate singularity corresponds to an envelope of wave surfaces, with a proposed vacuum extension.

Abstract

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.