AUTHOR=De Uday Chand , Shenawy Sameh , Abu-Donia H. M. , Turki Nasser Bin , Alsaeed Suliman , Syied Abdallah Abdelhameed 

TITLE=Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.800060

DOI=10.3389/fphy.2021.800060

ISSN=2296-424X

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 $%
f\left( R\right) $ gravity are studied. In this case, the forms of the
isotropic pressure $p$ and the energy density $\sigma $ 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.