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Null hypersurfaces in Lorentzian manifolds: I

Published online by Cambridge University Press:  24 October 2008

K. Katsuno
K. Katsuno
Affiliation:
Queen Elizabeth College, London
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Extract

This paper is concerned with geometrical properties of null hypersurfaces in Lorentzian manifolds. Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. First, the contravariant metric cannot immediately be defined, so the connection cannot be specified uniquely in the normal way. Secondly, the normal is a null vector lying in the tangent plane, which makes it necessary to look for some other vector to rig the hypersurface, and makes it impossible to normalise the normal in the usual way. These problems are considered in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 175 - 182
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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