Possibility of the Traversable Wormholes in the Galactic Halos within 4D Einstein–Gauss–Bonnet Gravity

Recently, there has been significant interest regarding the regularization of a $D\to 4$ limit of Einstein–Gauss–Bonnet (EGB) gravity. This regularization involves re-scaling the Gauss–Bonnet (GB) coupling constant as $\alpha /(D-4)$, which bypasses Lovelock's theorem and avoids Ostrogradsky instability. A noteworthy observation is that the maximally or spherically symmetric solutions for all the regularized gravities coincide in the $4D$ scenario. Considering this, the wormhole solutions in the galactic halos are investigated based on three different choices of dark matter (DM) profiles, such as Universal Rotation Curve, Navarro–Frenk–White, and Scalar Field Dark Matter with the framework of $4D$ EGB gravity. Also, the Karmarkar condition is used to find the exact solutions for the shape functions under different non-constant redshift functions. The energy conditions for each DM profile are discussed and the influence of GB coefficient $\alpha$ in violating energy conditions are noticed, especially null energy conditions. Further, some physical features of wormholes, viz. complexity factor, active gravitational mass, total gravitational energy, and embedding diagrams, have been explored.