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Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics
Umea Univ, Dept Phys, S-90187 Umea, Sweden.
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
Univ Minho, Dept Matemat Ciencia and Tecnol, P-4800058 Azurem, Guimaraes, Portugal.
2010 (Engelska)Ingår i: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 42, nr 1, s. 155-182Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we obtain complete agreement with the results obtained in intrinsic coordinates. We have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.

Ort, förlag, år, upplaga, sidor
2010. Vol. 42, nr 1, s. 155-182
Nyckelord [en]
Generalised invariant formalism; Pure radiation spacetimes; Karlhede invariant classification of spacetimes
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-52894DOI: 10.1007/s10714-009-0823-9OAI: oai:DiVA.org:liu-52894DiVA, id: diva2:285762
Tillgänglig från: 2010-01-13 Skapad: 2010-01-12 Senast uppdaterad: 2017-12-12

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Edgar, Brian

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