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One of the possible potential candidates for describing the universe's rapidexpansion is modified gravity. In the framework of the modified theory ofgravity $f(R,G)$, the present work features the materialization of anisotropicmatter, such as compact stars. Specifically, to learn more about the physicalbehavior of compact stars, the radial, and tangential pressures as well as theenergy 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, themodified 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 studyfocuses on graphical analysis of compact stars wherein the stability aspects,energy conditions, and anisotropic measurements are mainly addressed. Ourcalculation revealed that, for the positive value of parameter n of the model$f(G)$, all the six stars behave normally.

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