Abstract
The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.
Highlights
A concircular transformation was first coined by Yano in 1940 [1]
Motivated by these studies and many others, the main aim of this paper is to study concircularly flat and concircularly flat perfect fluid spacetimes in f(R) gravity
The energy-momentum tensor of a spacetime with divergence free concircular curvature tensor obeying f(R) gravity is of Codazzi type
Summary
A concircular transformation was first coined by Yano in 1940 [1]. Such a transformation preserves geodesic circles. R 2 gij κT ij, with κ being the Newtonian constant and T ij is the energy-momentum tensor [7]. These equations imply that the energy-momentum tensor Tij is divergence-free. Spacetimes with divergence free concircular curvature tensor in f(R) gravity are considered.
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