Junction conditions for null hypersurfaces

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Abstract
The authors derive an expression for the singular part of the stress-energy tensor on a hypersurface in spacetime in terms of the discontinuities in fundamental forms associated with the surface for both the non-null case, where the results are standard, and the null case. They then derive the minimum conditions which must be satisfied in order to glue two spacetimes together along such a hypersurface. In both cases, the essential requirement is only that the naturally induced (possibly degenerate) 3-metrics on the hypersurface must agree.

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