Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

TL;DR

This paper derives a new class of conformally flat spacetimes with pure radiation and a cosmological constant using the generalized invariant formalism, extending previous methods for Petrov types O and N.

Contribution

It introduces a method to handle spacetimes with isotropy freedom and rich Killing vector structures within the generalized invariant formalism, expanding the classification of pure radiation metrics.

Findings

Karlhede algorithm terminates at fourth derivative order

Spacetimes have one degree of null isotropy

Number of Killing vectors ranges from three to five

Abstract

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.