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

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a $\mathrm{\Lambda }$-term can be Ricci semi-symmetric without being conformally semi-symmetric.