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

TL;DR

This paper explores the theoretical possibility of traversable wormholes in galactic halos within 4D Einstein-Gauss-Bonnet gravity, analyzing different dark matter profiles and their impact on energy conditions and wormhole properties.

Contribution

It investigates wormhole solutions in 4D EGB gravity considering various dark matter profiles and examines how the GB coupling affects energy conditions and physical features.

Findings

GB coupling influences energy condition violations.

Wormhole solutions depend on dark matter profiles.

Physical features like mass and energy are analyzed.

Abstract

Recently, there has been significant interest regarding the regularization of a $D\rightarrow 4$ 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, we investigate the wormhole solutions in the galactic halos 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 was used to find the exact solutions for the shape functions under different non-constant redshift functions. We discussed the energy conditions for each DM profile and noticed the influence of GB coefficient $\alpha$ in violating energy conditions, 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.