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The present work is to introduce a new kind of modified gravitational theory,named as $f(\mathcal{R,G,T})$ (also $f(\mathcal{R,T,G})$) gravity, where$\mathcal{R}$ is the Ricci scalar, $\mathcal{G}$ is Gauss-Bonnet invariant and$\mathcal{T}$ is the trace of the energy-momentum tensor. With the help ofdifferent models in this gravity, we investigate some physical features ofdifferent relativistic compact stars. For this purpose, we develop theeffectively modified field equations, conservation equation, and the equationof motion for test particle. Then, we check the impact of additional force(massive test particle followed by a non-geodesic line of geometry) on compactobjects. Furthermore, we took three notable stars named as $Her X-1$,$SAXJ1808.4-3658$ and $4U1820-30$. The physical behavior of the energy density,anisotropic pressures, different energy conditions, stability, anisotropy, andthe equilibrium scenario of these strange compact stars are analyzed throughvarious plots. Finally, we conclude that the energy conditions hold, and thecore of these stars is so dense.

Compact Stars in $f(\mathcal{R,G,T})$ Gravity