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 subclas...

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Bibliographic Details
Published in:General relativity and gravitation 2014-10, Vol.46 (10), p.1797, Article 1797
Main Authors: Edgar, S. Brian, Bradley, Michael, Machado Ramos, M. Piedade
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Differential Geometry
generalised invariant formalism
Karlhede classification
Mathematical and Computational Physics
Physics
Physics and Astronomy
pure radiation spacetimes
Quantum Physics
Relativity Theory
Research Article
symmetries
teoretisk fysik
Theoretical
Theoretical Physics
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Summary: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.
ISSN:0001-7701
1572-9532
1572-9532
DOI:10.1007/s10714-014-1797-9