Wormhole geometries and energy conditions in linear and non-linear $f(Q,L_m)$ gravity

This study explores static and spherically symmetric wormhole configurations in an extended formulation of symmetric teleparallel gravity governed by $f(Q,L_m)=\alpha (-Q)+\beta L_m$ and $f(Q,L_m)=-Q+L_m^{\alpha }$ (where $Q$ is the non-metricity scalar, $L_m$ is the matter Lagrangian, and $\alpha ,\beta$ are constants). By varying the action with respect to the metric, we obtain the corresponding field equations. We conclude that the linear $f(Q,L_m)=\alpha (-Q)+\beta L_m$ framework successfully supports physically realistic wormholes without requiring extreme energy condition violations. It has been demonstrated that spacetime solutions violating both the radial and lateral null energy conditions in general relativity can nevertheless satisfy the NEC in $f(Q,L_m)$ gravity. Within non-linear $f(Q,L_m)$ gravity, non-exotic asymptotically flat wormhole solutions are derived using linear and asymptotically linear equations of state. Our results open new avenues to link modified gravity models with the observable astrophysical traits of exotic spacetimes.