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We find all Ricci semi-symmetric as well as all conformally semi-symmetricspacetimes. Neither of these properties implies the other. We verify that onlyconformally flat spacetimes can be Ricci semi-symmetric without beingconformally semi-symmetric and show that only vacuum spacetimes and spacetimeswith just a $\Lambda$-term can be Ricci semi-symmetric without beingconformally semi-symmetric.

Investigation of all Ricci semi-symmetric and all conformally semi-symmetric spacetimes