The Petrov and Kaigorodov-Ozsváth Solutions: Spacetime as a Group Manifold

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dc.creatorGibbons, Gary W.
dc.creatorGielen, Steffen
dc.date2008-02-27
dc.date2008-06-12
dc.date.accessioned2026-07-07T12:14:14Z
dc.date.available2026-07-07T12:14:14Z
dc.descriptionThe Petrov solution (for $Λ=0$) and the Kaigorodov-Ozsváth solution (for $Λ<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for the Kaigorodov-Ozsváth solution in the context of the adS/CFT correspondence. By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group. The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsváth solution. By applying the method of non-linear realisations to both algebras, we obtain a Lagrangian of Finsler type from the general first-order action in both cases. Interpreting the Petrov solution as the exterior solution of a rigidly rotating dust cylinder, we discuss the question of creation of CTCs by spinning up such a cylinder. We show geodesic completeness of the Petrov and Kaigorodov-Ozsváth solutions and determine the behaviour of geodesics in these spacetimes. The holonomy groups were shown to be given by the Lorentz group in both cases.
dc.description25 pages (latex), 3 figures, corrected a few minor errors
dc.identifierhttps://arxiv.org/abs/0802.4082
dc.identifierhttp://arxiv.org/abs/0802.4082
dc.identifierClass.Quant.Grav.25:165009,2008
dc.identifierdoi:10.1088/0264-9381/25/16/165009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211120
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleThe Petrov and Kaigorodov-Ozsváth Solutions: Spacetime as a Group Manifold
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