An analysis of the problems (associated with discontinuities in the components of the momentum-energy tensor and with discontinuities in the second derivatives of the components of the metric tensor) for spaces in which the Einstein field equations of general relativity hold. Explicit solutions are obtained for values of the discontinuities in the second derivatives of the components of the metric tensor in terms of the discontinuities in the components of the momentum-energy tensor, where this tensor is left arbitrary. The equations describing the evolution of these discontinuities are obtained and reduced, and the equations of motion are evaluated across the resulting discontinuity surfaces.
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