Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism
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.
KeywordsGeneralised invariant formalism Pure radiation spacetimes Karlhede classification Symmetries
This research was partially supported by the Research Center of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPETE, and by the Portuguese Funds through FCT—Fundação para a Ciência e Tecnologia within the Project Est-C/MAT/UI0013/2011. MB wishes to thank the Center of Mathematics of the University of Minho, for supporting a visit to this university, and the Department of Mathematics and Applications for their hospitality.
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