Analysis of W3 Curvature Tensor in Modified Gravity and Its Cosmological Implications

In this study, we investigated the geometric and physical implications of the W3 curvature tensor within the framework of f(R,G) gravity. We found the sufficient conditions for W3 flat spacetimes with constant scalar curvature to be de Sitter (R>0) or Anti-de Sitter (R<0) models. The properties of isotropic spacetime in the modified gravity framework were also investigated. Furthermore, we explored spacetimes with a divergence-free W3 curvature tensor. The necessary and sufficient condition for a W3 Ricci recurrent and parallel spacetime to transform into an Einstein spacetime was determined. Finally, we analyzed the role of the W3 curvature tensor in black hole thermodynamics within f(R,G) gravity.