Type O pure radiation metrics with a cosmological constant

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.

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Cited by in corpus (4)

• Explicit algebraic classification of Kundt geometries in any dimension
• On conformally flat and type N pure radiation metrics
• Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant
• Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism