Integration using invariant operators:Conformally flat radiation metrics

TL;DR

This paper introduces a novel method for deriving conformally flat radiation metrics using invariant differential operators, expanding the toolkit for analyzing such spacetimes in general relativity.

Contribution

The work develops a new approach employing invariant operators to systematically obtain conformally flat radiation metrics, generalizing previous methods.

Findings

Derived the general conformally flat radiation metric using invariant operators.

Constructed involutive tables for derivatives in the Karlhede classification.

Provided a systematic procedure for metric derivation in conformally flat spacetimes.

Abstract

A new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalisation of the GHP operators) which are invariant under null rotations and spin and boosts. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of metrics.