Geometric Effects of Linear Matter-Curvature Coupling on Relativistic Stellar Structures

We examine the geometric and dynamical properties of relativistic compact stars in a gravity model characterized by a linear matter–curvature coupling of the form f(R, T) = R + 2γT. The inclusion of the matter-geometry coupling parameter γ introduces deviations from standard General Theory of Relativity (GR), allowing additional geometric effects that can influence the stability and structural properties of ultra-dense compact stars while remaining compatible with observational constraints. The corresponding modified field equations are formulated for a static spherically symmetric spacetime representing the stellar interior. A complete set of exact solutions to the modified f(R, T) field equations is obtained by employing the class-one embedding condition in conjunction with the Vaidya-Tikekar form, which is adopted as the seed ansatz for the metric potential g rr . The unknown constants appearing in the solutions are determined through smooth matching between the interior spacetime and the exterior Schwarzschild geometry at the stellar boundary. The physical viability of the resulting configurations is examined by analyzing several relevant constraints, including the behavior of metric functions, thermodynamic quantities, the equation of state parameter, energy conditions, and stability criteria. We further explore key structural characteristics such as the mass function, compactness, surface redshift, and moment of inertia. The model is applied to three representative compact star candidates, namely Cen X–3, PSR J1903+327, and Vela X–1. The obtained numerical estimates for the mass–radius ratio, surface redshift, and relativistic adiabatic index remain consistent with standard astrophysical expectations. These results indicate that the proposed framework provides a viable description of compact stellar configurations within modified gravity.