Astrophysical implications of two viable charged anisotropic solutions for the compact star 4U 1820-30 in matter-geometry coupled <i>f</i> ( <i>R</i> ) gravity

Two distinct singularity-free charged anisotropic interior models are presented in this study within the context of the matter-geometry coupled f(R) gravity. To achieve this, the field equations are derived under the proposed model and we find them highly non-linear. By considering certain constraints, we get two differential equations whose solutions are obtained using the exact integration. To determine the integration constants in our solutions, we enforce a smooth matching between the interior solution and the vacuum exterior at the boundary. We further apply the zero radial pressure condition at the boundary to engage the model parameters in these constants. The observational data of a particular star, 4U 1820-30, is then used to analyze the physical properties of both of our models under various model parameters’ values. In this theoretical framework, the obtained solutions consistently meet the essential requirements for physically realistic compact stars, and thus paving the way for future research in this domain.