Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in $f\left(T\right)$-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for $f\left(T\right)$-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure $f\left(T\right)$ gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.