A note on some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes and their conformal vector fields in <i>f</i>(<i>R</i>) theory of gravity

Hussain, Farrukh; Kara, A. H.; Ramzan, Muhammad

doi:10.1142/s0217732319500792

Cited by 27 publications

(4 citation statements)

References 39 publications

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“…Moreover, it is applied in [39] the non-vacuum field equations of f (R) to a spherically symmetric space-time having an unequal metric potential. It is also worth mentioning that investigations of conformal symmetries for some remarkable space-times in the f (R)-gravity, such as static plane symmetric space-times, static spherically symmetric spacetimes, static cylindrically symmetric space-times, spatially homogeneous rotating space-times, Bianchi type II space-times, Kantowski-Sachs symmetric space-times, and non-static plane symmetric space-times, were realized in [40][41][42][43][44][45][46]). In the papers just mentioned, the authors found solutions of field equations using different fluid matters in the f (R)-gravity and obtained conformal vector fields for the derived solutions using some algebraic techniques.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

Syied,

De,

Bin Turki

et al. 2024

Phys. Scr.

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In this work, characterizations of vacuum solutions of f(R)-gravity are established in a space-time whose Z tensor is of Codazzi type. We prove that the associated covector of a (PZS)_{n} space-time is an eigenvector of the Ricci tensor, with an eigenvalue equals zero. Additionally, it satisfies compatibility conditions with both the Riemann and Weyl tensors. It is proved that a (PZS)_{n} space-time satisfying f(R)-gravity vacuum solutions is a generalized Friedmann-Robertson-Walker space-time. If n=4, it becomes a Friedmann-Robertson-Walker space-time.

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Section: Introductionmentioning

confidence: 99%

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

Syied,

De,

Bin Turki

et al. 2024

Phys. Scr.

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“…The CS also gives a deep insight into the space-time geometry that further helps to describe the associated kinematics as well as dynamics. With these properties, special attention has been given to the study of the CVFs in MTs of gravitation in the last few years [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88]. Continuing this stream of work, we are conducting a study to classify the static SS perfect fluid space-times via CVFs in the f (T) theory of gravity.…”

Section: Introductionmentioning

confidence: 99%

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

Hussain¹

2022

Commun. Theor. Phys.

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In this paper, we classify static spherically symmetric (SS) perfect fluid space-times via conformal vector fields (CVFs) in the f(T) gravity. For this analysis, we first explore static SS solutions by solving the Einstein field equations (EFEs) in the f(T) gravity. Secondly, we implement a direct integration technique to classify the resulting solutions. During the classification, there arose twenty cases. Studying each case thoroughly, we come to know that in three cases, the space-times under consideration admit proper CVFs in the f(T) gravity. In one case, the space-time admits proper homothetic vector fields (HVFs) whereas, in the rest of the sixteen cases, either the space-times become conformally flat, or it admits Killing vector fields (KVFs).

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“…Shamir [39] has studied the vacuum Kantowski-Sachs and Bianchi type III spacetimes in the f (R) theory of gravity. The paper [47] deals with the conformal vector fields of Kantowski-Sachs and Bianchi III spacetimes filled with perfect fluid in the f (R) theory of gravity. The paper [35] conducted a study of these two models in the f (R, T ) theory.…”

Section: Introductionmentioning

confidence: 99%

“…The paper [35] conducted a study of these two models in the f (R, T ) theory. In [39], and [47], the vacuum field equations are solved by assuming the expansion scalar Θ to be proportional to the shear scalar σ. The article [48] treats a perturbed Kantowski-Sachs model using numerical integration.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe

Datta,

Guha

2021

Preprint

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In this paper, we apply the Regge-Wheeler formalism in our study of axial and polar gravitational waves in Kantowski-Sachs universe. The background field equations and the linearised perturbation equations for axial and polar modes are derived in presence of matter. To find the analytical solutions, we analyse the propagation of waves in vacuum spacetime. The background field equations in absence of matter are first solved by assuming that the expansion scalar Θ to be proportional to the shear scalar σ (so that the metric coefficients are given by the relation a = b n , where n is an arbitrary constant). Using the method of separation of variables, the axial perturbation parameter h 0 (t, r) is obtained from its wave equation. The other perturbation h 1 (t, r) is then determined from h 0 (t, r). We observe that the anisotropy of the background spacetime is responsible for the damping of the axial waves propagating through it. On the other hand, the polar perturbation equations are much more involved compared to their FLRW counterparts, as well as to the axial perturbations in Kantowski-Sachs background. The polar equations contain complicated couplings among the perturbation variables. In both the axial and polar cases, the radial and temporal solutions for the perturbations separate out as product. The perturbation equations in presence of matter show that the axial waves can cause perturbations only in the azimuthal velocity of the fluid without deforming the matter field. But the polar waves must perturb the energy density, the pressure and also the non-azimuthal components of the fluid velocity. The propagation of axial and polar gravitational waves in Kantowski-Sachs and Bianchi I spacetimes is found to be more or less similar in nature.

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A note on some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes and their conformal vector fields in f(R) theory of gravity

Cited by 27 publications

References 39 publications

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe

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