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

TL;DR

This paper classifies all spacetimes that are Ricci semi-symmetric or conformally semi-symmetric, clarifying their relationships and identifying specific conditions under which these properties coincide or differ.

Contribution

It provides a complete classification of Ricci and conformally semi-symmetric spacetimes and clarifies their independence and specific conditions for their occurrence.

Findings

Only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric.

Vacuum spacetimes and those with only a cosmological constant are Ricci semi-symmetric but not conformally semi-symmetric.

The properties of Ricci semi-symmetry and conformal semi-symmetry do not imply each other.

Abstract

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 $\Lambda$-term can be Ricci semi-symmetric without being conformally semi-symmetric.