Compact relativistic geometries in $f(R,G)$ gravity

One of the possible potential candidates for describing the universe's rapid expansion is modified gravity. In the framework of the modified theory of gravity $f(R,G)$, the present work features the materialization of anisotropic matter, such as compact stars. Specifically, to learn more about the physical behavior of compact stars, the radial, and tangential pressures as well as the energy density of six stars namely $Her X-1$, $SAXJ1808.4-3658$, $4U1820-30$, $PSR J 1614 2230$, $VELA X-1$, and $Cen X-3$ are calculated. Herein, the modified theory of gravity $f(R,G)$ is disintegrated into two parts i.e. the $\tanh$ hyperbolic $f(R)$ model and the three different $f(G)$ model. The study focuses on graphical analysis of compact stars wherein the stability aspects, energy conditions, and anisotropic measurements are mainly addressed. Our calculation revealed that, for the positive value of parameter n of the model $f(G)$, all the six stars behave normally.