Covariant derivatives on null submanifolds Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/76537423x

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  • The degenerate nature of the metric on null hypersurfaces creates many difficulties when attempting to define a covariant derivative on null submanifolds. This dissertation investigates these challenges and provides a technique for defining a connection on null hypersurfaces in some cases. 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. In addition, a condition on the Ricci tensor is given to determine when this construction can be used. All of the results are motivated through a sequence of examples of null surfaces on which the covariant derivative is defined. Finally, a covariant derivative operator is given for the class of spherically symmetric hypersurfaces.
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  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2010-12-15T23:11:52Z (GMT) No. of bitstreams: 1 HickethierDonL2010.pdf: 320552 bytes, checksum: c74d15260f85c2dc66e37d645298d6d0 (MD5)
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