Graduate Thesis Or Dissertation
 

Covariant derivatives on null submanifolds

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https://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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file details HickethierDonL2010.pdf 2017-08-14 Público Baixar