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=9

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=<p>The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in <italic>f</italic>(<italic>R</italic>) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:mfenced></mml:math></inline-formula> gravity are studied. In this case, the forms of the isotropic pressure <italic>p</italic> and the energy density <italic>σ</italic> are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in <italic>f</italic>(<italic>R</italic>) 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.</p>