A discussion of Einstein's general relativity field equations, the study of which is usually begun by assuming certain particular forms for the metric tensor. In the presence of a general momentum-energy tensor that admits jump discontinuities, the question arises as to the consistency of the assumed metric structure in regions where the jumps in the momentum-energy tensor occur. To answer this question, the author examines the continuation of orthogonal structure across surfaces of discontinuity in the momentum-energy tensor and analyzes the problems of several massive bodies of finite extent. It is concluded that, although orthogonal structure for problems of the second and third classes can generally be continued, the problems of the first class will only admit orthogonal structure, everywhere in the space under very particular circumstances.
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