Dynamical behavior of stellar structures in $f(\mathcal{G})$ gravity

In the context of modified $f(\mathcal G)$ gravity, we study the appearance of anisotropic compact stellar objects. The space–time geometry is characterized by the metric potentials, and to solve the field equations, we consider their specific form known as the Tolman–Kuchowicz space–time. The obtained solutions are free of singularities and satisfy all requirements for stellar objects. We consider the observational data for models of the stars Cen X-3, EXO 1785-248, and LMC X-4, and taking these data into account, we obtain the values of the physical parameters from the matching conditions for the interior Tolman–Kuchowicz space–time and the exterior Schwarzschild metric. In addition, we discuss some physical attributes of anisotropic compact stellar structures to verify the physical validity and stability of the proposed model. We perform a three-dimensional graphical analysis that allows obtaining a representation of the physical behavior of these compact objects. We note that all three compact objects correspond to physically accepted models.