Abstract
The constraint equations are well-understood for hypersurfaces which are either everywhere non-null or null everywhere. The corresponding form of the equations is very different in both cases. In this paper, I discuss a general framework capable of analyzing the intrinsic and extrinsic geometry of general hypersurfaces of a spacetime. This framework is then applied to derive the form of the constraint equations in this general context. As an application, I will generalize the Israel equations for spacetime shells to the case when the shell is allowed to have varying causal character.
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