Proper semiconformal symmetries of spacetimes with divergengence-free semiconformal curvature tensor

Abstract

In the present paper, we show that a four-dimensional spacetime manifold admitting a proper semiconformal symmetry is semiconformally flat or of the type $N$. It is also shown that a four-dimensional spacetime with divergence-free semiconformal curvature tensor admitting a proper semiconformal symmetry is locally of the type $O$ or has four distinct principal null directions. In both the cases, we found that the spacetime admits an infinitesimal semiconformal Killing vector field then the scalar curvature of the spacetime vanishes.