On curvature properties of Som-Raychaudhuri spacetime

Abstract

Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasi-Einstein, generalized Roter type, $Ein(3)$ manifold satisfying $R.R=Q(S,R)$, $C\cdot C=\frac{2a^2}{3}Q(g,C)$, and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Gödel spacetime and Som-Raychaudhuri spacetime.

arXiv commentThe paper contained 14 pages