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Junction conditions for null hypersurfaces. (English) Zbl 0609.53033

We 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 our results are standard, and the null case. We 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.

MSC:

53B50 Applications of local differential geometry to the sciences
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C99 General relativity
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