About: Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions

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About: Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://iopscience.iop.org/0264-9381/28/14/145010/
Description	Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg–Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions. Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg–Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions. (en)
Title	Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions (en)
skos:prefLabel	Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions (en)
skos:notation	RIV/00216224:14310/11:00064682!RIV13-MSM-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(LC505)
http://linked.open...iv/cisloPeriodika	14
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Taghavi-Chabert, Arman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	218555
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/11:00064682
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Robinson manifolds; algebraically special higher-dimensional spacetimes (en)
http://linked.open.../riv/klicoveSlovo	Robinson manifolds algebraically special higher-dimensional spacetimes
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[D295FDE72EAA]
http://linked.open...i/riv/nazevZdroje	Classical and Quantum Gravity
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Eduard Čech Center for Algebra and Geometry
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	28
http://linked.open...iv/tvurceVysledku	Taghavi-Chabert, Arman
http://linked.open...ain/vavai/riv/wos	000291789300010
issn	0264-9381
number of pages	32 (xsd:int)
http://bibframe.org/vocab/doi	10.1088/0264-9381/28/14/145010
http://localhost/t...ganizacniJednotka	14310

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