Covariant derivatives on null submanifolds |
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Authors: | Don Hickethier Tevian Dray |
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Institution: | 1. Department of Mathematics, Flathead Valley Community College, Kalispell, MT, 59901, USA 2. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA
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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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Keywords: | |
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