Traversable wormhole solutions with non-exotic fluid in framework of $f(Q)$ gravity

Abstract

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC's are not violated signifying the standard matter in the WH geometry. In the present article we are trying to find the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity $f(Q)$ where $Q$ is the non metricity scalar which defines the gravitational interaction. We will examine the wormhole geometries for three forms of function $f(Q)$. First is the linear form $f(Q)=\alpha Q$, second a non -linear form $f(Q)=\alpha Q^2 + \beta$ and third one a more general quadratic form $f(Q)=\alpha Q^2 + \beta Q + \gamma$ with $\alpha$, $\beta$ and $\gamma$ being the constants. For all the three cases the shape function is taken as $b(r) = {\frac{r_{0}\ln(r+1)}{\ln({r_0}+1)}}$ where $r_0$ is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and the stability of the wormhole geometry.