On ricci symmetric generalized quasi einstein spacetimes

Güler, Si̇nem; Demirbağ, Sezgin Altay

doi:10.18514/mmn.2015.1447

Cited by 15 publications

(6 citation statements)

References 10 publications

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“…being κ the Einstein's gravitational constant, T is the energymomentum tensor( [32], [27]) describing the matter content of the spacetime. From (15) and (18) we infer that…”

Section: An A(pzs) 4 Spacetime With Codazzi Type Of Z Tensormentioning

confidence: 99%

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On a type of spacetimes

Jin

Chand

2019

Filomat

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In the present paper we characterize a type of spacetimes, called almost pseudo Z-symmetric spacetimes A(PZS) 4. At first, we obtain a condition for an A(PZS) 4 spacetime to be a perfect fluid spacetime and Roberson-Walker spacetime. It is shown that an A(PZS) 4 spacetime is a perfect fluid spacetime if the Z tensor is of Codazzi type. Next we prove that such a spacetime is the Roberson-Walker spacetime and can be identified with Petrov types I, D or O[3], provided the associated scalar φ is constant. Then we investigate A(PZS) 4 spacetimes satisfying divC = 0 and state equation is derived. Also some physical consequences are outlined. Finally, we construct a metric example of an A(PZS) 4 spacetime.

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“…being κ the Einstein's gravitational constant, T is the energymomentum tensor( [32], [27]) describing the matter content of the spacetime. From (15) and (18) we infer that…”

Section: An A(pzs) 4 Spacetime With Codazzi Type Of Z Tensormentioning

confidence: 99%

“…Recently Mantica and Molinari published a survey article on GRW spacetime [26]. Several authors studied spacetimes in different way such as ( [15], [16], [20], [24], [34]) and many others. In [10] Chaki and Ray studied spacetimes with covariant constant energy momentum tensor.…”

Section: Introductionmentioning

confidence: 99%

On a type of spacetimes

Jin

Chand

2019

Filomat

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“…A spacetime is the stage of present modeling of the physical world: a torsion-less, time oriented Lorentzian manifold. For details of spacetime, we cite ( [5], [18], [22]- [25], [27], [28], [39], [46], [55]).…”

Section: Physical Applications: (Wbs) 4 Spacetimesmentioning

confidence: 99%

On weakly B symmetric pseudo Riemannian manifolds and its applications

Alberto

Chand

Jin

2021

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The object of the present paper is to study weakly B symmetric manifolds (WBS)n. At first some geometric properties of (WBS)n(n > 2) have been studied. Finally, we consider (WBS)4 spacetimes. They turn out to be both perfect and imperfect fluids Robertson-Walker space-times : an equation of state is provided in the first case, and in the second the nature of the bulk viscosity pressure is pointed out. Also, we construct an example of a (WBS)4.

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“…Many researchers have studied the physical and geometrical properties of perfect fluid and Einstein spacetimes endowed with solitons, and established several remarkable results. For instance, we cite ( [23][24][25][26][27][28][29]) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Ricci solitons on general relativistic spacetimes

Suh

Chaubey²

2023

Phys. Scr.

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The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci and gradient Ricci solitons. It is proven that if the metric of a general relativistic spacetime (M4, ξ) admitting a special unit timelike vector field ξ is an almost Ricci soliton (g, ξ, λ), then (M4, ξ) is a perfect fluid spacetime, and almost Ricci soliton (g, ξ, λ) on (M4, ξ) becomes shrinking Ricci soliton. We prove that a general relativistic perfect fluid spacetime equipped with a special unit timelike vector field together with a Ricci soliton is an Einstein spacetime. In this sequel, we also prove that the Ricci soliton is shrinking, soliton vector field is Killing and the scalar curvature of the perfect fluid spacetime is constant. It is proven that a general relativistic perfect fluid spacetime together with a Ricci soliton is a generalized Robertson-Walker (GRW) spacetime. The existence of gradient Ricci solitons on general relativistic spacetimes are established. We also construct a non-trivial example of general relativistic spacetime equipped with a special unit timelike vector field, and verify some of our theorems.

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On ricci symmetric generalized quasi einstein spacetimes

Cited by 15 publications

References 10 publications

On a type of spacetimes

On a type of spacetimes

On weakly B symmetric pseudo Riemannian manifolds and its applications

Ricci solitons on general relativistic spacetimes

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