Wormhole configuration with viable equation of state in f(Q) gravity

Abstract

In this paper, we present asymptotically flat wormhole geometries in the context of $f\left(Q\right)$ gravity theory, where $Q$ is non-metricity scalar, by assuming a particular equation of state (EOS) $\rho =\Psi [P_r+(n-2)P_{\perp }]$, where $\Psi$ denotes a EOS parameter and $n$ is any integer. In this regard, we have established two different wormhole models by solving the EOS assuming the particular values for the parameter $n$, say for $n=1$ and $n=3$, and investigate the effect of EOS parameter on the wormhole geometries. The conducted analysis shows that the energy density is consistently positive for the wormhole models and the null energy condition is violated which indicates the presence of exotic matter. Furthermore, we have also developed a third model by assuming a specific shape function that satisfies all the necessary conditions of wormholes. Moreover, these solutions are found to be stable utilizing an equilibrium condition. Additionally, we go over the phenomenon of the complexity factor for all wormhole models and conclude that, for larger values of the radial coordinate, it approaches zero which shows the isotropic behavior of pressure and homogeneity of energy density.