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Covariant Derivatives on Null Submanifolds

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dc.creator Hickethier, Don
dc.creator Dray, Tevian
dc.date.accessioned 2012-10-15T23:12:56Z
dc.date.available 2012-10-15T23:12:56Z
dc.date.issued 2012-01
dc.identifier.citation Hickethier, D., & Dray, T. (2012). Covariant derivatives on null submanifolds. General Relativity and Gravitation, 44(1), 225-238. doi: 10.1007/s10714-011-1275-6 en_US
dc.identifier.uri http://hdl.handle.net/1957/34426
dc.description This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://www.springerlink.com/content/0001-7701/. en_US
dc.description.abstract The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes, conformal transformations are used to construct a covariant derivative on null hypersurfaces, and a condition on the Ricci tensor is given to determine when this construction can be used. Several examples are given, including the construction of a covariant derivative operator for the class of spherically symmetric hypersurfaces. en_US
dc.language.iso en_US en_US
dc.publisher Springer en_US
dc.relation.ispartofseries General Relativity and Gravitation en_US
dc.relation.ispartofseries Vol. 44 no. 1 en_US
dc.subject Null hypersurfaces en_US
dc.subject Null submanifolds en_US
dc.subject Covariant derivative en_US
dc.subject Conformal transformation en_US
dc.subject Asymptotically flat spacetime en_US
dc.subject Killing normal vector en_US
dc.title Covariant Derivatives on Null Submanifolds en_US
dc.type Article en_US
dc.description.peerreview yes en_US
dc.identifier.doi 10.1007/s10714-011-1275-6

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