On curvature properties of Som–Raychaudhuri spacetime

Abstract

Abstract. Som-Raychaudhuri [32] 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-quasiEinstein, generalized Roter type, Ein(3) manifold satisfying R.R = Q(S, R), C · C = 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.

Curvature properties of a special type of pure radiation metrics

“…We note that Som-Raychaudhuri metric [40] and Robinson-Trautman metric [34] are 2-quasi-Einstein whereas Gödel metric [15] is Ricci simple.…”

“…, [5], [8], [38], [41], [42], [51]) A semi-Riemannian manifold M is said to be H- We note that Som-Raychaudhuri metric [40] and Robinson-Trautman metric [34] are 2-quasi-Einstein whereas Gödel metric [15] is Ricci simple. [39]) A semi-Riemannian manifold M is said to be Ein(2), Ein (3) and Ein (4) respectively if…”

Curvature properties of Robinson–Trautman metric

“…It may be noted that Som-Raychaudhuri spacetime is 2-quasi-Einstein but not quasi-Einstein [68]. For recent results on 2-quasi-Einstein manifolds, we refer the reader to see [25], [26] and [28] .…”

“…last four decades generalized concept of pseudosymmetry by Deszcz has been characterized and classified with existence in several papers by Deszcz and his coauthors (see [11], [12], [17], [24], [63] and also references therein); and the pseudosymmetric spacetimes were studied by Deszcz and his co-authors (see, [14], [30], [36]). It may be noted that Gödel spacetime ( [33], [37]), Som-Raychaudhuri spacetime ( [68], [78]), Reissner-Nordström spacetime [45] and Robertson-Walker spacetimes ( [3], [13], [34]), are models of different pseudosymmetric type structures.…”

“…Lanczos potentials of the metric are studied by Ahsan and Bilal [2]. In the study of differential geometry, pseudosymmetric structures play an important role due their applications in relativity and cosmology (see, [14], [30], [33], [36], [68], [76] and also references therein). It is noteworthy to mention that the present paper is unconventional as by considering a physically relevant metric, viz., Robinson-Trautman metric, we would like to investigate the curvature restricted geometric structures admitted by such metric.…”