Type O pure radiation metrics with a cosmological constant

TL;DR

This paper completes the classification of conformally flat pure radiation spacetimes with a non-zero cosmological constant using the generalised invariant formalism, revealing diverse symmetry subclasses.

Contribution

It extends previous work by analyzing the case b3 + au   0, demonstrating the effectiveness of the GIF in such spacetimes and identifying their symmetry properties.

Findings

Classified all conformally flat pure radiation spacetimes with b3 + au    0

Found a variety of subclasses with different numbers of Killing vectors

Validated the use of GIF for spacetimes with a single null direction

Abstract

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors.