Curvature properties of Gödel metric

A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a vacuum spacetime. In the present paper we investigate the curvature properties of special type of pure radiation metrics presented by Ludwig and Edgar. It is shown that such a pure radiation spacetime is semisymmetric, Ricci simple, R-space by Venzi and its Ricci tensor is Riemann compatible. It is also proved that its conformal curvature 2-forms and Ricci 1-forms are recurrent. We also present a pure radiation type metric and evaluate its curvature properties along with the form of its energy momentum tensor. It is interesting to note that such pure radiation type metric is Ein(3) and 3-quasi-Einstein. We also find out the sufficient conditions for which this metric represents a generalized pp-wave, pure radiation and perfect fluid. Finally we made a comparison between the curvature properties of Ludwig and Edgar's pure radiation metric and pp-wave metrics.

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“…Definition 2.2. A symmetric (0, 2)-tensor E on M is said to be cyclic parallel (resp, Codazzi type) (see, [15], [16] and references therein) if…”

Section: Curvature Restricted Geometric Structuresmentioning

confidence: 99%

Curvature properties of a special type of pure radiation metrics

Shaikh

Kundu

Ali

et al. 2019

Journal of Geometry and Physics

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“….. In view of the above endomorphisms we have various curvature tensors given as follows ( [17], [29], [19], [25]):…”

Section: Curvature Restricted Geometric Structuresmentioning

confidence: 99%

“…Recently Deszcz et al [17] studied the geometric properties of Gödel metric and showed that the Gödel spacetime is Ricci simple. We recall that both the Gödel metric and Som-Raychaudhuri metric are of Gödel type.…”

Section: Som-raychaudhuri Spacetime As a Gödel Type Spacetimementioning

confidence: 99%

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On curvature properties of Som–Raychaudhuri spacetime

Shaikh

Kundu

2016

J. Geom.

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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.

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“…connected semi-Riemannian smooth manifold M equipped with the metric g. Suppose ∇ and R are respectively the operator of covariant differentiation and Reimann curvature tensor of M. Now we define the (1, 3)-tensors C s pqr , P s pqr , W s pqr and K s pqr of M respectively as[15,20,29,68] …”

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confidence: 99%

Curvature properties of Nariai spacetimes

Shaikh

Ali

Alkhaldi

et al. 2020

Int. J. Geom. Methods Mod. Phys.

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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.

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Curvature properties of Gödel metric

Abstract: The main aim of this paper is to investigate the geometric structures admitting by the Gödel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of Gödel metric.

Cited by 38 publications

References 63 publications

Curvature properties of a special type of pure radiation metrics

Curvature properties of a special type of pure radiation metrics

On curvature properties of Som–Raychaudhuri spacetime

Curvature properties of Nariai spacetimes

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