Anisotropic Compact Stars in f(𝒢,T) Gravity via the Karmarkar Condition: Physical Viability and Stability Analysis

In this paper, we study anisotropic compact stellar configurations in the framework of modified [Formula: see text] gravity using the Karmarkar embedding condition using Durgapal metric potential. Exact interior solutions for the power-law model [Formula: see text] are obtained and smoothly matched to the exterior Schwarzschild spacetime by means of the Israel–Darmois junction conditions. We apply the model to the observed compact stars SMC X-4, Cen X-3, PSR J0348+0432, PSR J0740+6620 and EXO 1785-248. The energy density, radial pressure and tangential pressure are finite at the centre of the star and decrease monotonically towards the surface, with the positive anisotropic factor aiding equilibrium against gravitational collapse. The proposed solutions satisfy the null and strong energy conditions which guarantee the physical viability of the matter distribution. Further, the causality condition, Herrera’s cracking condition and the adiabatic index are within the acceptable physical limits which further establishes the stability. Further, the predicted mass–radius relation, compactness and surface redshift satisfy the corresponding astrophysical bounds, which proves the agreement with realistic neutron-star models. These results show that the joint Karmarkar condition with [Formula: see text] gravity gives a consistent and physically admissible framework for the modeling of anisotropic compact stars.