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arXiv · 1108.2332

Covariant Derivatives on Null Submanifolds

Don Hickethier·Tevian Dray
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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.

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Don Hickethier, Tevian Dray. 2011-08-11. Covariant Derivatives on Null Submanifolds. https://doi.org/10.1007/s10714-011-1275-6

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