Covariant Derivatives on Null Submanifolds Public Deposited

http://ir.library.oregonstate.edu/concern/defaults/np193981z

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/.

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  • 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.
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  • 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
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  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2012-10-15T23:12:56Z (GMT) No. of bitstreams: 1 DrayTevianMathematicsCovariantDerivativesNull.pdf: 138870 bytes, checksum: 141bbb7fc353a2ae18f4c46d781afc7d (MD5)
  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2012-10-15T23:10:02Z No. of bitstreams: 1 DrayTevianMathematicsCovariantDerivativesNull.pdf: 138870 bytes, checksum: 141bbb7fc353a2ae18f4c46d781afc7d (MD5)
  • description.provenance : Made available in DSpace on 2012-10-15T23:12:56Z (GMT). No. of bitstreams: 1 DrayTevianMathematicsCovariantDerivativesNull.pdf: 138870 bytes, checksum: 141bbb7fc353a2ae18f4c46d781afc7d (MD5) Previous issue date: 2012-01

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