In this article we obtain wormhole solutions in the recently proposed extension of symmetric teleparallel gravity called $f(Q,T)$ gravity. Here, the gravitational Lagrangian $L$ is defined by an arbitrary function $f$ of $Q$ and $T$ (where $Q$ is the non-metricity scalar, while $T$ is the trace of the energy-momentum tensor). In this study, we obtain the field equations for a static spherically symmetric wormhole metric in the context of a general $f(Q,T)$ gravity. We study the wormhole solutions with (i) linear EoS and (ii) anisotropy relation. We adopt two different forms of $f(Q,T)$ (a) linear $f(Q,T)=\alpha Q+\beta T$ and (b) non-linear $f(Q,T)=Q+\lambda Q^2+\eta T$ to investigate these solutions. We investigate the various energy conditions to look for preservation and violation among the solutions that we obtained. We find that NEC is violated in both cases of our assumed forms of $f(Q,T)$. Finally, we perform the stability analysis using Tolman-Oppenheimer-Volkov (TOV) equation.

No abstract

In this study, we have conducted an analysis of traversable wormhole solutions within the framework of linear $f(Q, T) = \alpha Q + \beta T$ gravity, ensuring that all the energy cnditions hold for the entire spacetime. The solutions presented in this study were derived through a comprehensive analytical examination of the parameter space associated with the wormhole model. This involved considering the exponents governing the redshift and shape functions, as well as the radius of the wormhole throat ($r_0$), the redshift function value at the throat ($\phi_0$), and the model parameters ($\alpha$ and $\beta$). Also, we have established bounds on these free parameters that guarantee the satisfaction of the energy conditions throughout spacetime and have also provided two solutions. Further, we have used the Israel junction condition to see the stability of a thin-shell around the wormhole. We have also calculated the NEC criteria and potential for such a thin-shell and how it varies with the chosen shape function.

No abstract