Tolman-Oppenheimer-Volkoff equations in Ricci Inverse Gravity with Matter Coupling

We propose a modified theory of gravity by extending the Einstein-Hilbert action with an inverse Ricci scalar 𝒜 = g μν (ℛ μν ) −1 and a trace-matter coupling 𝒯. A detailed derivation of the modified field equations is provided. Additionally, we apply the theory to static, spherically symmetric compact stars and derive the generalized Tolman-Oppenheimer-Volkoff equations in terms of an effective energy-momentum tensor. Even for isotropic matter, inverse Ricci corrections generate effective pressure anisotropy. Using a polytropic equation of state, we analyze the effective density and pressure profiles and show that inverse curvature and trace coupling significantly enhance the central density and pressure compared to General Relativity. These results indicate that Ricci inverse gravity with trace coupling can substantially affect the internal structure of compact stars in the strong field regime.