An empty spacetime has zero or constant Ricci Scalar (depending on the cosmological constant). Is there a theorem which guarantees that such a spacetime should be Minkowski or dS/AdS? In other words, can there be non-uniformly curved spacetimes which are empty everywhere?
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Schwarzchild metric has $R=0$ and is not maximally symmetric spacetime.
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$\begingroup$ I mean an empty spacetime everywhere! Schwarzschild spacetime has a central mass! Are there solutions other than Minkowski, dS and AdS which satisfy Einstein equations everywhere with zero energy momentum tensor? $\endgroup$– NematCommented Nov 11, 2019 at 6:11