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 (ECs), focusing on the null ECs 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.

中文翻译：

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虫洞的光偏转及其在修正对称平行引力形式中由暗物质引起的阴影


我们探讨了在 f（Q） 引力背景下暗物质晕中可穿越虫洞形成的可能性。我们根据 Bose-Einstein 凝聚态、Navarro-Frenk-White 和伪等温物质密度剖面，获得了具有各向异性物质源的精确虫洞解。值得注意的是，我们提出了一种由这些暗物质支持的新型虫洞解决方案，使用密度分布和转速的表达式以及修改后的场方程来计算虫洞的红移和形状函数。通过一组特定的参数，我们证明了我们提出的虫洞解在渐近背景下满足耀斑条件。此外，我们还研究了能量条件 （EC），重点关注虫洞喉咙处的零 EC，提供了可行区域和负区域的图形表示。我们的研究还检查了在各种暗物质模型存在下虫洞的阴影，揭示了较高的中心密度会导致阴影更靠近喉咙，而较低的值则具有相反的效果。此外，我们探索了光遇到这些虫洞时的偏转，特别注意到光在喉咙处的偏转接近无穷大，那里的引力场非常强。