Holographic dark matter profiles and their impact on wormhole formation and redshift in dRGT gravity

Abstract

Inspired by holographic dark energy models, this work delves into a comprehensive examination of various energy density profiles as potential sources required for the existence of traversable wormhole solutions. In particular, we emphasize our analysis of wormhole solutions within the dRGT massive gravity framework. Notably, we propose novel wormhole solutions sustained by dark matter, utilizing the density profiles and rotational velocity expressions in conjunction with the modified field equations. These formulations facilitate the derivation of the redshift and shape functions, providing a thorough framework for analyzing the geometry and physical properties of the wormhole. The solution demonstrates a traversable wormhole that violates the null energy condition within specific ranges of the free parameters. Using embedding diagrams, we investigate the geometry of these wormholes and determine the stability of the solutions by evaluating the equilibrium conditions. Finally, the deflection angle $\hat{\alpha }\left(r_0\right)$ remains entirely negative for the parameter ranges $\lambda \in [18,25]$, $\chi \in [1.5,2]$, and $m\in [18,20]$. This indicates that photons experience repulsive gravitational effects, resulting in light rays being deflected outward from the wormholes instead of being drawn in.