Structure of Quark Stars in f(R) Gravity

We explore $f\left(R\right)$ gravity, a classical extension of general relativity, and evaluate its applicability to compact stars. As a modification of Einstein's theory, $f\left(R\right)$ gravity serves as a useful framework for investigating gravitational effects in ultra-relativistic regimes where (standard) general relativity may break down, while remaining consistent with it in weak-field limits. In this work, we derive a second-order modified Tolman–Oppenheimer–Volkoff (MTOV) system, consisting of four coupled second-order differential equations, for general $f\left(R\right)$ gravity. This formulation is applied to static, spherically symmetric strange quark stars modeled using the MIT Bag equation of state. We propose two $f\left(R\right)$ models, each incorporating a single parameter that governs the deviation from general relativity. The MTOV equations are solved numerically using the Runge–Kutta-Fehlberg method, and the results are compared to those obtained in general relativity. Our findings demonstrate that $f\left(R\right)$ gravity can yield distinct and physically meaningful modifications to the properties of compact stars. We further examine the contributions of second- and higher-order corrections in the scalar-tensor sector of the gravitational action.