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In this paper, I examine the gravitational action for spacetimes with nonsmooth boundaries. By two independent techniques, I derive the contribution to the gravitational action of spacelike and timelike two-surfaces on the boundary at which the unit normal changes discontinuously. I discuss the relationship between constraints imposed at such two-surfaces and their contribution to the gravitational action. I derive the form of the action and the juncture conditions appropriate to cases in which a spacetime includes a singular matter distribution whose world history corresponds to a timelike two-dimensional surface.
Geoff Hayward (1993) studied this question.