Compact stars coupled with dark matter via decoupling process in extended symmetric teleparallel gravity: Mass-radius limit with observational data

This article analyzes the anisotropic charged solutions for compact stars within the framework of extended symmetric teleparallel gravity, wherein anisotropy has been generated in compact stars via gravitational decoupling. The renowned Tolman-Finch-Skea solution and Buchdahl metric are utilized to derive two sets of solutions for a pure extended symmetric teleparallel gravity, specifically within the context of pure f ( Q, T ) gravity. Meanwhile, the decoupled system is addressed using the Einasto spike dark matter density profile, which introduces anisotropy into the system. We evaluate the viability of modeling charge-dark matter compact stars with the Einasto spike density profile. Within this paradigm, we delineate the temporal aspect of the Θ 0 0 -field sector to accurately quantify the impact of dark matter on the gravitational matter source. An detailed graphical examination of the structural factors and stability demonstrates that both models, given the selected parameters, yield well-behaved and physically consistent results. The findings of this investigation are both feasible and commendable, offering significant insights. The equilibrium of forces, derived from the modified TOV equations, illustrates a stable balance among gravitational, electrostatic, and hydrostatic factors. The analysis encompassed the modeling of three distinct stellar candidates, incorporating their mass-radius relation constraints for GW190814 (2.5–2.67), PSR J 2215 + 5135 ( 2 . 28 − 0.09 + 0.10 ), and PSR J 1810 + 1744 (2.13 ± 0.04).—utilizing observable astrophysical data, the corresponding radii were determined to fall within the range [9.7, 12.58] km. The mass-radius relationship indicates a maximum mass, with associated radii closely aligning with observational limits.