A note on pseudo Ricci symmetric space-times admitting a conformal vector field

Abstract

In this paper, we characterize a pseudo Ricci symmetric space-time admitting a proper conformal vector field. At first, it is shown that under certain restriction on the associated scalar σ, such a space-time is of vanishing scalar curvature. Also, we prove that such a space-time with harmonic Weyl tensor is vacuum. Consequently, it is concluded that this space-time is of Petrov type N and represents a plane-fronted gravitational wave with parallel rays. Finally, it is shown that a pseudo Ricci symmetric space-time admitting a homothetic vector field represents a stiff matter fluid.