A study of dark matter interactions with wormhole metrics in the context of f(Q) gravity

Abstract

This study explores the impact of dark matter within the f(Q) gravity framework, emphasizing its role in supporting traversable wormhole solutions. By considering anisotropic matter sources modeled through Bose–Einstein condensate and Einasto density profiles, we derive a novel class of wormhole solutions. The shape function of the wormholes is constructed using the density profile equation and modified field equations, providing a robust foundation for these solutions. The analysis includes the incorporation of a traceless fluid equation of state, which reveals the intricate influence of dark matter on the existence and stability of wormhole structures. To ensure physical plausibility, specific parameter choices are made, confirming that the proposed solutions meet all essential conditions for traversable wormholes. Furthermore, energy conditions are systematically evaluated under four distinct scenarios, and embedding techniques are applied to gain deeper insights into the wormhole geometries. Next, we extend our study to analyze the volume integral quantifier and the anisotropic effect. This work provides a comprehensive perspective on the interplay between dark matter and f(Q) gravity, shedding light on the feasibility of exotic spacetime configurations. Finally, the stability of the derived wormhole solutions is verified using the Tolman–Oppenheimer–Volkoff equation, demonstrating a balance of forces and the physical stability of the models.