Alignment and algebraically special tensors in Lorentzian geometry

Simple item page
dc.creatorMilson, R.
dc.creatorColey, A.
dc.creatorPravda, V.
dc.creatorPravdova, A.
dc.date2004-01-04
dc.date2004-07-20
dc.date.accessioned2026-07-07T11:42:56Z
dc.date.available2026-07-07T11:42:56Z
dc.descriptionWe develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the PND equation. In 4D, this recovers the usual Petrov types. For higher dimensions, we prove that, in general, a Weyl tensor does not possess aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the geometric properties of the corresponding alignment variety.
dc.description19 pages. Revised presentation
dc.identifierhttps://arxiv.org/abs/gr-qc/0401010
dc.identifierhttp://arxiv.org/abs/gr-qc/0401010
dc.identifierInt.J.Geom.Meth.Mod.Phys.2:41-61,2005
dc.identifierdoi:10.1142/S0219887805000491
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201061
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleAlignment and algebraically special tensors in Lorentzian geometry
dc.typetext

Files

Collections

arXiv