On curvature properties of Som-Raychaudhuri spacetime

TL;DR

This paper investigates the curvature properties of Som-Raychaudhuri spacetime, revealing its geometric structures and comparing it with G"odel spacetime, thereby enhancing understanding of its mathematical and physical characteristics.

Contribution

It characterizes the curvature restricted geometric structures of Som-Raychaudhuri spacetime and establishes its properties as a 2-quasi-Einstein, generalized Roter type, $Ein(3)$ manifold.

Findings

Som-Raychaudhuri spacetime is a 2-quasi-Einstein manifold.

It satisfies $R.R = Q(S,R)$ and $C\cdot C = \frac{2a^2}{3} Q(g,C)$.

Ricci tensor is cyclic parallel and Riemann compatible.

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 G\"odel spacetime and Som-Raychaudhuri spacetime.