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The assumption that {T^};=0 in curved space-time is questioned. Field equations are given which are consistent with the assumption {T^};=R, , and which reduce to the Einstein equations when =0. The equations are equivalent to the Einstein equations in empty space-time, but differ from them in the presence of matter. Applications to cosmology, stellar structure, and collapsing objects are suggested.
Peter Rastall (Fri,) studied this question.