Minimally deformed anisotropic stars in dark matter halos under EGB-action

Abstract In this paper, we introduce an anisotropic model using a dark matter (DM) density profile in Einstein–Gauss–Bonnet (EGB) gravity using a gravitational decoupling method introduced by Ovalle (Phys Rev D 95:104019, 2017), which has provided an innovative approach for obtaining solutions to the EGB field equations for the spherically symmetric structure of stellar bodies. The Tolman and Finch–Skea (TFS) solutions of two metric potentials, $$g_{tt}$$ g tt and $$g_{rr}$$ g rr , have been used to construct the seed solution. Additionally, the presence of DM in DM halos distorts spacetime, causing perturbations in the $$g_{rr}$$ g rr metric potential, where the quantity of DM is determined by the decoupling parameter $$\beta $$ β . The physical validity of the solution, along with stability and equilibrium analysis, has also been performed. Along with stability and equilibrium analysis, the solution’s physical validity has also been examined. Additionally, we have shown how both constants affect the physical characteristics of the solution. Using a $$M{-}R$$ M - R diagram, it has been described how the DM component and the GB constant affect the maximum permissible masses and their corresponding radii for various compact objects. Our model predicts the masses beyond the $$2~M_{\odot }$$ 2 M ⊙ and maximum radii $$11.92^{+0.02}_{-0.01}$$ 11 . 92 - 0.01 + 0.02 and $$12.83^{+0.01}_{-0.02}$$ 12 . 83 - 0.02 + 0.01 for larger value of $$\alpha $$ α under density order $$10^{15}~\text {g}/\text {cm}^3$$ 10 15 g / cm 3 and $$10^{14}~\text {g}/\text {cm}^3$$ 10 14 g / cm 3 , respectively, while the radii become $$11.96^{+0.01}_{-0.01}$$ 11 . 96 - 0.01 + 0.01 and $$12.81^{+0.01}_{-0.02}$$ 12 . 81 - 0.02 + 0.01 for larger value of $$\beta $$ β .