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Null shells are a useful geometric construction to study the propagation ofinfinitesimally thin concentrations of massless particles or impulsive waves.In this paper, we determine and study the necessary and sufficient conditionsfor the matching of two spacetimes with respective null embedded hypersurfacesas boundaries. Whenever the matching is possible, it is shown to depend on adiffeomorphism between the set of null generators in each boundary and a scalarfunction, called step function, that determines a shift of points along thenull generators. Generically there exists at most one possible matching but insome circumstances this is not so. When the null boundaries are totallygeodesic, the point-to-point identification between them introduces a freedomwhose nature and consequences are analyzed in detail. The expression for theenergy-momentum tensor of a general null shell is also derived. Finally, wefind the most general shell (with non-zero energy, energy flux and pressure)that can be generated by matching two Minkowski regions across a nullhyperplane. This allows us to show how the original Penrose's cut-and-pasteconstruction fits and connects with the standard matching formalism.

Null shells: general matching across null boundaries and connection with cut-and-paste formalism