Spherically symmetric vacuum solutions of modified field equations in \(f(R, \Sigma , T)\)-gravity

This study examines spherically symmetric static empty space solutions within the framework of the \(f(R, \Sigma , T)\)-gravity, where \(f(R, \Sigma , T)\) is a general function of the scalar curvature R, the torsion scalar \(\Sigma \) and the trace of the energy–momentum tensor T. We reduce the modified Einstein equations to a single equation and demonstrate how to construct exact solutions across various \(f(R, \Sigma , T)\)-gravity models. Notably, we establish that for a broad class of models, including the \(f(R, \Sigma , T)=R+\Sigma +2 \eta T\) model, the Schwarzschild metric serves as an exact solution to the field equations, alongside other classes of solutions. We discuss the significance of these findings in the context of solar system constraints on \(f(R, \Sigma , T)\) theories of gravity. Additionally, the effects of space–time torsion and particle spin on the solar system are also explored.