We consider the general relativity field equations in two‐ and three‐dimensional space–times. We find that in a two‐dimensional space–time we can have curvature but not matter. In a three‐dimensional space–time we find that empty space must be flat, that a de Sitter solution exists, and that finite mass distributions with constant surface density must have zero ’’surface tension.’’ Finally, an expanding dust‐filled universe turns out to be like Milne’s model.

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