About: Explicit algebraic classification of Kundt geometries in any dimension

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1088/0264-9381/30/12/125007
Description	We present an algebraic classification, based on the null alignment properties of the Weyl tensor, of the general Kundt class of spacetimes in arbitrary dimension D for which the non-expanding, non-twisting, shear-free null direction k is a (multiple) Weyl aligned null direction (WAND). No field equations are used, so that the results apply not only to Einstein's gravity and its direct extension to higher dimensions, but also to any metric theory of gravity which admits the Kundt spacetimes. By an explicit evaluation of the Weyl tensor in a natural null frame we demonstrate that all Kundt geometries are of type I(b) or more special, and we derive simple necessary and sufficient conditions under which k becomes a double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, IIi, IIIi, D(a), D(b), D(c) and D(d). The corresponding conditions are surprisingly clear and expressed in an invariant geometric form. Some of them are always satisfied in four dimensions. To illustrate our classification scheme, we apply it to the most important subfamilies of the Kundt class, namely the pp-waves, the VSI spacetimes, and the generalization of the Bertotti-Robinson, Nariai, and Plebanski-Hacyan direct-product spacetimes of any dimension. We present an algebraic classification, based on the null alignment properties of the Weyl tensor, of the general Kundt class of spacetimes in arbitrary dimension D for which the non-expanding, non-twisting, shear-free null direction k is a (multiple) Weyl aligned null direction (WAND). No field equations are used, so that the results apply not only to Einstein's gravity and its direct extension to higher dimensions, but also to any metric theory of gravity which admits the Kundt spacetimes. By an explicit evaluation of the Weyl tensor in a natural null frame we demonstrate that all Kundt geometries are of type I(b) or more special, and we derive simple necessary and sufficient conditions under which k becomes a double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, IIi, IIIi, D(a), D(b), D(c) and D(d). The corresponding conditions are surprisingly clear and expressed in an invariant geometric form. Some of them are always satisfied in four dimensions. To illustrate our classification scheme, we apply it to the most important subfamilies of the Kundt class, namely the pp-waves, the VSI spacetimes, and the generalization of the Bertotti-Robinson, Nariai, and Plebanski-Hacyan direct-product spacetimes of any dimension. (en)
Title	Explicit algebraic classification of Kundt geometries in any dimension Explicit algebraic classification of Kundt geometries in any dimension (en)
skos:prefLabel	Explicit algebraic classification of Kundt geometries in any dimension Explicit algebraic classification of Kundt geometries in any dimension (en)
skos:notation	RIV/00216208:11320/13:10188962!RIV14-GA0-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA202/09/0772), P(GAP203/12/0118)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Švarc, Robert Podolský, Jiří
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	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	74285
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10188962
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	integration; spaces; invariants; field-equations; vacuum spacetimes; n solutions; conformally flat; gravitational-waves; cosmological constant; pure radiation metrics (en)
http://linked.open.../riv/klicoveSlovo	spaces gravitational-waves conformally flat field-equations n solutions pure radiation metrics vacuum spacetimes invariants integration cosmological constant
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[2AB0920363C6]
http://linked.open...i/riv/nazevZdroje	Classical and Quantum Gravity
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Current problems of gravitation, general relativity and relativistic astrophysics Spacetimes and Fields in Higher Dimensional and Classical Gravity
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	30
http://linked.open...iv/tvurceVysledku	Podolský, Jiří Švarc, Robert
http://linked.open...ain/vavai/riv/wos	000319664000008
issn	0264-9381
number of pages	25 (xsd:int)
http://bibframe.org/vocab/doi	10.1088/0264-9381/30/12/125007
http://localhost/t...ganizacniJednotka	11320

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