Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents

Abstract

In this paper, the metric approach of f (R) theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f (R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f (R) gravity for some appropriate f (R) model, which turns out to be a constant quantity.

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

“…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.…”

Localized energy associated with Bianchi-Type VI universe in $f(R)$ theory of gravity

“…Making use of the generalized Landau-Liftshitz prescription for the Schwarzschildde Sitter universe, Multamäki et al [50] calculated energy distribution for some well known f (R) gravity models including constant curvature scalar. Later, Amir and Naheed [51] considered a spatially homogeneous rotating spacetime solution of f (R) gravity to calculate Landau-Liftshitz energy density. Moreover, using some wellknown f (R) theory suggestions, Salti et al [52] also discussed energy-momentum localization problem for Gödel-Type metrics.…”

Non-Vacuum Plane Symmetric Solutions and their Energy Contents in f (R) Gravity

“…Recently, Jamil and his co-workers explored spatially homogenous rotating solution [33] in and locally rotationally symmetric solutions [34] and their energy contents. Now, we are intend to extend the work done by Sharif and Shamir [27] to the case of non-vacuum static plane symmetry solutions…”