Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity

Amir, M. Jamil; Sattar, Sadia

doi:10.1007/s10773-013-1865-z

Cited by 14 publications

(6 citation statements)

References 44 publications

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“…-gravity [1,2,3]. Here is called as Gauss-Bonnet curvature invariant which is defined by a combination formed from the Riemann curvature tensor which are contractions of the = Ricci curvature tensor and the = Ricci curvature scalar as = − 4 + [4,5,6,7,8]. In the literature; in order to simplify the equations of ( , ) , Locally Rotationally Symmetric (LRS) Bianchi-Type models based on the assumption = (or = or = ) are often considered to reduce the number of unknowns [9,10,11].…”

Section: Introductionmentioning

confidence: 99%

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

Güler

Güdekli

2021

AJR2P

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In this paper, we study the -gravitation theory under the assumption that the standard matter-energy content of the universe is a perfect fluid with linear barotropic equation of state within the framework of Bianchi-Type III model from the class of homogeneous and anisotropic universe models. However, whether such a restriction lead to any contradictions or inconsistencies in the field equations will create an issue that needs to be examined. Under the effective fluid approach, we will be concerned mainly the field equations in an orthonormal tetrad framework with an equimolar and examined the situation of establishing the functional form of together with the scale factors, which are their solutions. Unlike similar studies, which are very few in the literature, instead of assuming preliminary solutions, we determined the consistency conditions of the field equations by assuming the matter energy content of the universe as an isotropic perfect fluid for Bianchi-Type III.

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Section: Introductionmentioning

confidence: 99%

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

Güler

Güdekli

2021

AJR2P

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“…Constant curvature solutions, i.e. f ′ (R)R − 2f (R) = 0, were found with cylindrical symmetry [15,16], plane-symmetry [17], and local rotational symmetry [18]. Spherically symmetric solutions in connection to black-holes and the rotation curve of galaxies are studied in [19].…”

Section: Introductionmentioning

confidence: 99%

General properties of f(R) gravity vacuum solutions

Capozziello

Mantica

Molinari

2020

Int. J. Mod. Phys. D

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General properties of vacuum solutions of [Formula: see text] gravity are obtained by the condition that the divergence of the Weyl tensor is zero and [Formula: see text]. Specifically, a theorem states that the gradient of the curvature scalar, [Formula: see text], is an eigenvector of the Ricci tensor and, if it is timelike, the spacetime is a Generalized Friedman–Robertson–Walker metric; in dimension four, it is Friedman–Robertson–Walker.

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“…Faraoni and Nadeau [35] have discussed some important f (R) models along with their stability conditions. Jamil and his collaborators [36,37] obtained the spatially homogeneous rotating solutions and locally rotating spacetimes in f (R) gravity and the energy contents are obtained for non-trivial solution for particular f (R) model. Silva et al [38] proposed a six-dimensional string-like braneworld built from a warped product between a 3-brane and the Hamilton cigar soliton space.…”

Section: Introductionmentioning

confidence: 99%

Energy-Momentum Distribution of Six-Dimensional Geometric Model of Gravitational Field

Ali¹,

Amir²

2019

Universal Journal of Mathematics and Applications

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Much work has been done in exploring the energy-momentum distribution of different four-dimensional spacetimes using different prescriptions. In this paper, we intend to explore the energy and momentum density of six-dimensional geometric model of the gravitational field. The model was constructed by postulating a six-dimensional spacetime manifold with a structure of spacetime of absolute parallelism. For this purpose, we consider the metric representing the geometric model and use five prescriptions, namely, Einstein, Landau-Lifshitz, Bergmann-Thomson, Papapetrou, and Möller in the framework of General Relativity. The energy and momentum turn out to be well defined and finite. The comparison of the results shows that Einstein and Bergmann-Thomson prescriptions yield same energy-momentum densities but different from the other three prescriptions. It is mentioning here that the energy vanishes in the case of Möller's prescription and the momentum densities become zero in all the cases.

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Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity

Cited by 14 publications

References 44 publications

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

General properties of f(R) gravity vacuum solutions

Energy-Momentum Distribution of Six-Dimensional Geometric Model of Gravitational Field

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