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The formalism of hypersurface data is a framework to study hypersurfaces ofany causal character abstractly (i.e. without the need of viewing them asembedded in an ambient space). In this paper we exploit this formalism to studythe general problem of matching two spacetimes in a fully abstract manner, asthis turns out to be advantageous over other approaches in several respects. Wethen concentrate on the case when the boundaries are null and prove that thewhole matching is determined by a diffeomorphism $\varphi$ on the abstract dataset. By exploiting the gauge structure of the formalism we find explicitexpressions for the gravitational/matter-energy content of any null thin shell.The results hold for arbitrary topology. A particular case of interest is whenmore than one matching is allowed. Assuming that one such matchings has alreadybeen solved, we provide explicit expressions for thegravitational/matter-energy content of any other shell in terms of the knownone. This situation covers, in particular, all cut-and-paste constructions,where one can simply take as known matching the trivial re-attachment of thetwo regions. We include, as an example, the most general matching of tworegions of the (anti-)de Sitter or Minkowski spacetime across a totallygeodesic null hypersurface.

Abstract Formulation of the Spacetime Matching Problem and Null Thin Shells