Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

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.

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

“…This groundbreaking theory not only promises to explain the observed accelerated expansion of the Universe without the need for dark energy but also opens the door to exploring exotic phenomena such as wormholes, black holes, and the nature of dark matter. With its mind-bending implications and potential to reshape our understanding of the universe, f (R) modified gravity theory stands as a captivating frontier in modern physics, engaging the minds of scientists and enthusiasts alike (for more details about this subject see [4][5][6][7][8][9][10][11] ). Among the many notable results achieved recently in this field, we would like to mention only a few.…”