Dynamics of relativistic wormholes in the presence of dark matter density profile within f(Q,T) gravity

In this paper, we study the characteristics of wormhole models in a particular gravity theory, namely $f\left(Q,T\right)=\sigma Q+\lambda T$. Here, we derived the wormhole models by using dark matter profiles that are Einasto spike and Pseudo isothermal that is ${\rho }_{ES}={\rho }_{0}exp\left(\frac{-2}{\zeta }\left({\left(\frac{r}{r_s}\right)}^{\zeta }-1\right)\right)$ and ${\rho }_{PI}=\frac{\omega }{1+\mu r^2}$ respectively. The obtained solutions for the wormhole’s shape function satisfy the necessary metric requirements. This study focuses on how the parameters $\sigma$ and $\lambda$ affect the equilibrium state of the wormhole solution and violations of energy conditions. We found that every model deviates from the null energy threshold, suggesting the existence of exotic matter that is required for the wormholes to be stable. Furthermore, we deciphered the geometry of wormhole models using embedding diagrams. Additionally, we investigated the repulsive effect of gravity. When the geodesic motion around the wormholes is examined, it is discovered that the photon deflection angle is negative, suggesting the existence of gravity’s repulsive effect for both models.