Deflection of light by wormholes and its shadow due to dark matter within modified symmetric teleparallel gravity formalism

TL;DR

This paper investigates traversable wormholes supported by dark matter within modified symmetric teleparallel gravity, analyzing their properties, energy conditions, shadows, and light deflection to understand their observational signatures.

Contribution

It presents novel exact wormhole solutions supported by dark matter profiles in $f(Q)$ gravity and studies their shadows and light deflection effects.

Findings

Wormhole solutions satisfy flare-out conditions with specific parameters.

Higher dark matter densities lead to shadows closer to the wormhole throat.

Light deflection approaches infinity at the wormhole's throat.

Abstract

We explore the possibility of traversable wormhole formation in the dark matter halos in the context of $f(Q)$ gravity. We obtain the exact wormhole solutions with anisotropic matter source based on the Bose-Einstein condensate, Navarro-Frenk-White, and pseudo-isothermal matter density profiles. Notably, we present a novel wormhole solution supported by these dark matters using the expressions for the density profile and rotational velocity along with the modified field equations to calculate the redshift and shape functions of the wormholes. With a particular set of parameters, we demonstrate that our proposed wormhole solutions fulfill the flare-out condition against an asymptotic background. Additionally, we examine the energy conditions, focusing on the null energy conditions at the wormhole's throat, providing a graphical representation of the feasible and negative regions. Our study also examines the wormhole's shadow in the presence of various dark matter models, revealing that higher central densities result in a shadow closer to the throat, whereas lower values have the opposite effect. Moreover, we explore the deflection of light when it encounters these wormholes, particularly noting that light deflection approaches infinity at the throat, where the gravitational field is extremely strong.