About: On the Goldberg–Sachs theorem in higher dimensions in the non-twisting case

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study a generalization of the shearfree part’ of the Goldberg–Sachs theorem for Einstein spacetimes admitting a non-twisting multiple Weyl aligned null direction (WAND) in n>5 spacetime dimensions. The form of the corresponding optical matrix ρ is restricted by the algebraically special property in terms of the degeneracy of its eigenvalues. In particular, there necessarily exists at least one multiple eigenvalue, and further constraints arise in various special cases. For example, when ρ is non-degenerate and certain (boost weight zero) Weyl components do not vanish, all eigenvalues of ρ coincide and such spacetimes thus correspond to the Robinson–Trautman class. On the other hand, in certain degenerate cases all non-zero eigenvalues can be distinct. We also present explicit examples of Einstein spacetimes admitting some of the permitted forms of ρ, including examples violating the optical constraint’. We study a generalization of the shearfree part’ of the Goldberg–Sachs theorem for Einstein spacetimes admitting a non-twisting multiple Weyl aligned null direction (WAND) in n>5 spacetime dimensions. The form of the corresponding optical matrix ρ is restricted by the algebraically special property in terms of the degeneracy of its eigenvalues. In particular, there necessarily exists at least one multiple eigenvalue, and further constraints arise in various special cases. For example, when ρ is non-degenerate and certain (boost weight zero) Weyl components do not vanish, all eigenvalues of ρ coincide and such spacetimes thus correspond to the Robinson–Trautman class. On the other hand, in certain degenerate cases all non-zero eigenvalues can be distinct. We also present explicit examples of Einstein spacetimes admitting some of the permitted forms of ρ, including examples violating the optical constraint’. (en)
Title	On the Goldberg–Sachs theorem in higher dimensions in the non-twisting case On the Goldberg–Sachs theorem in higher dimensions in the non-twisting case (en)
skos:prefLabel	On the Goldberg–Sachs theorem in higher dimensions in the non-twisting case On the Goldberg–Sachs theorem in higher dimensions in the non-twisting case (en)
skos:notation	RIV/67985840:_____/13:00391346!RIV14-GA0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP203/10/0749)
http://linked.open...iv/cisloPeriodika	7
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Pravda, Vojtěch Pravdová, Alena Ortaggio, Marcel
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	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	93883
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00391346
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Einstein spacetimes; Goldberg-Sachs theorem (en)
http://linked.open.../riv/klicoveSlovo	Goldberg-Sachs theorem Einstein spacetimes
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[131FB1239276]
http://linked.open...i/riv/nazevZdroje	Classical and Quantum Gravity
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	General relativity in higher dimensions
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	30
http://linked.open...iv/tvurceVysledku	Pravda, Vojtěch Pravdová, Alena Ortaggio, Marcello
http://linked.open...ain/vavai/riv/wos	000316227500016
issn	0264-9381
number of pages	38 (xsd:int)
http://bibframe.org/vocab/doi	10.1088/0264-9381/30/7/075016

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