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Covariant Derivatives on Null Submanifolds Public Deposited

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https://ir.library.oregonstate.edu/concern/articles/np193981z

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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.
  • Keywords: Null hypersurfaces, Asymptotically flat spacetime, Covariant derivative, Conformal transformation, Null submanifolds, Killing normal vector
  • Keywords: Null hypersurfaces, Asymptotically flat spacetime, Covariant derivative, Conformal transformation, Null submanifolds, Killing normal vector
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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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  • 44
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  • 1
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