Curvature properties of Nariai spacetimes

Abstract

This article is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition ∇R = 0 is satisfied and it also admits the pseudosymmetric type curvature conditions C · R = (1+L0) 6r 2 0 Q(g, R) and P · R = − 1 3 Q(S, R). Moreover, it is 4-dimensional Roter type, 2-quasi-Einstein and generalized quasi-Einstein manifold. The energy-momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist a class of generalized recurrent type manifolds which is semisymmetric.2010 Mathematics Subject Classification. 53B20, 53B25, 53B30, 53B50, 53C15, 53C25, 53C35.

Geometrical Properties of a Point-like Global Monopole Spacetime

“…We note that Morris-Thorne spacetime [103] and Gödel spacetime [28] are Ricci simple manifolds, Robertson-Walker spacetime [26] and Siklos spacetime [29] are quasi-Einstein manifolds, Kantowski-Sachs spacetime [84] and Som-Raychaudhuri spacetime [25] are 2-quasi Einstein manifolds and Kaigorodov spacetime [29] is an Einstein manifold. For curvature properties of Robinson-Trautman metric, Melvin magnetic metric and generalized pp-wave metric, etc., we refer the reader to see [30,[104][105][106].…”

“…We mention that Vaidya-Bonner spacetime [106] and Lifshitz spacetime [110] are generalized Roter type manifold, and Nariai spacetime [105] and Melvin magnetic spacetime [109] are Roter type manifold. Definition 2.5.…”

Analytical model on mass limit of strange stars

“…Nariai IV metric has also been used to describe neutron stars Lattimer (2001 by Moustakidis (2017). Shaikh et al Shaikh (2020) studied the curvature properties of a charged Nariai type spacetime and found that such a metric is not locally symmetric but semi symmetric, and its Ricci tensor is neither Codazzi nor cyclic parallel or recurrent but generalized recurrent. Carlos Batista Batista (2016) presented some solutions which are made of the direct product of several 2-spaces of constant curvature.…”