Kohler-Chao Interior Solutions for Compact Stellar Objects in f(R, G) Gravity

In this work, we investigate the internal structure and physical features of compact stars in the background of modified gravity, specifically within f ( R, G ) gravity, where R represents the Ricci scalar and G denotes the Gauss–Bonnet invariant. The interior spacetime of the stellar configuration is described by the Kohler–Chao metric, which provides a suitable geometric representation for dense compact objects. Our analysis considers ten well-known compact star candidates, namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. To incorporate higher-curvature effects, the functional form of f ( R, G ) is decomposed into two independent contributions, f 1 ( R ) and f 2 ( G ), representing the Ricci scalar and Gauss–Bonnet sectors, respectively. For the R -dependent part, we adopt the Hu–Sawicki type model, while three different models, namely logarithmic and power-law models, are considered for the Gauss–Bonnet contribution. This reconstruction gives three distinct modified gravity models used to study the different features of compact stellar configurations. Using these models, we study the physical viability of the stellar structures by examining anisotropic pressure content, equilibrium scenario through the Tolman–Oppenheimer–Volkoff equation, energy conditions, and stability conditions. The obtained results demonstrate that the energy density, radial pressure, tangential pressure, and anisotropy remain well-behaved throughout the stellar interior for all considered stars. The analysis indicates that the proposed f ( R, G ) models together with the Kohler–Chao interior solution provide physically consistent and stable configurations for compact stars within the modified gravity framework.