Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity - De, Uday Chand; Shenawy, Sameh; Abu-Donia, H. M.; Turki, Nasser Bin; Alsaeed, Suliman; Syied, Abdallah Abdelhameed (Frontiers in Physics, 2022)
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 $% f\left( R\right) $ 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.