Geometry of W3-curvature tensor in f(R)-gravity

R. Prasad, A. Verma, V. S. Yada

In this paper, we explore the behaviour of W3-flat curvature tensor in f(R)-gravity. We describe W3-flat curvature tensor perfect fluid spacetime solutions of f(R)-gravity. It is noticed that after the establishment of W3-flat geometries of spacetime, we have found that the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of W3-conservative spacetime geometries in f(R))-gravity theory. We establish that the spacetime becomes a generalized Robertson-Walker spacetime with a shear, whirl, and acceleration independent perfect fluid with a particular form of expansion scalar presented in terms of scale factor. Moreover, f(R)-gravity model for W3-curvature tensor has been constructed to explain the different energy conditions with free parameter. We also study the behaviour of scale factor 'a' of the universe with the chosen model. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 223-237