A study of wormhole geometries in symmetric teleparallel gravity

Abstract

In this manuscript, we find the exact solutions of asymptotically flat wormhole (WH) geometry in the
background of symmetric $f(Q)$ gravity (vanishing curvature and torsion) where the non-metricity term
$Q$ is accountable for fundamental interaction. In this scenario, we choose two different $f(Q)$
gravity models (logarithmic and exponential) along with the special choice of shape function
$b(r)=\frac{r}{\exp(\gamma(r-r_{0}))}$, and redshift function $\phi(r)=\frac{r_{0}}{2r}$. Here,
$\gamma$ affects the radius of curvature of WH. Under this scenario, we analyze the viability of
the shape function and energy constraints of the WH solutions for each model. For both models,
we determine the validity regions of energy conditions under some parameter spaces of the model
parameters. The allowed parameter spaces for logarithmic and exponential models are illustrated
in Tables I and II, respectively. The validity region for the null energy condition represents that
WH geometry in chosen $f(Q)$ gravity models is supported by ordinary matter while exotic matter
elsewhere. Furthermore, we represent the WH construction by embedding diagrams and
shows that the derived WH solutions are stable for the allowed range of model parameters. Finally,
it is concluded that such particular modified gravity can give us a more realistic and stable
WH geometry.