Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism

TL;DR

This paper classifies conformally flat pure radiation spacetimes with a negative cosmological constant using GHP formalism, revealing null isotropy effects on symmetries and identifying existing Killing vectors.

Contribution

It provides a complete invariant classification of these spacetimes and extends symmetry analysis to cases with null isotropy using GHP formalism.

Findings

Metrics possess one null isotropy degree affecting symmetry structure

Explicit Killing vectors are identified for various subclasses

No homothetic Killing vectors are present in these spacetimes

Abstract

A complete and simple invariant classification of the conformally flat pure radiation metrics with a negative cosmological constant that were obtained by integration using the generalised invariant formalism is presented. We show equivalence between these metrics and the corresponding type O subclass of the more general spacetime studied by Siklos. The classification procedure indicates that the metrics possess a one degree of null isotropy freedom which has very interesting repercussions in the symmetry analysis. The Killing and homothetic vector analysis in GHP formalism is then generalised to this case were there is only one null direction defined geometrically. We determine the existing Killing vectors for the different subclasses that arise in the classification and compare these results to those obtained in the symmetry analysis performed by Siklos for a larger class of metrics with Ricci tensor representing a pure radiation field and a negative cosmological constant. It is also shown that there are no homothetic Killing vectors present.