Modelling self-gravitating systems in f(R,G) gravity with anisotropic pressure and Tolman-Kuchowicz background

The present study offers a comprehensive analysis of anisotropic matter distributions and various physical properties of compact stars within the framework of $f(R,G)$-gravity. To thoroughly explore these aspects, we focus on three specific compact stellar objects: Her X-1 (CS1), SAX J1808.4-3658 (CS2), and 4U 1820-30 (CS3). Using three distinct models of $f(R,G)$-gravity, we compute the relevant physical characteristics of these stars. For a systematic approach, the $f(R,G)$-gravity framework is decomposed into two components: $f_1\left(R\right)$ and $f_2\left(G\right)$. The R-dependent term, $f_1\left(R\right)$, is modelled following the Hu-Sawicki formalism, while the G-dependent term, $f_2\left(G\right)$, incorporates logarithmic and power-law formulations, leading to three viable gravitational models. We employ graphical analysis to examine the physical behaviour of these compact stars under the proposed modified gravity scenarios.