Traversable wormholes in $\boldsymbol{f(Q)}$ gravity: Energy conditions, stability and quasinormal modes

Abstract

We investigate static and spherically symmetric traversable wormhole solutions in the framework of $f(Q)$ gravity by considering a power-law model of the form $f(Q)=\gamma(-Q)^m$. By adopting an anisotropic matter distribution and imposing an equation of state relating the radial pressure and energy density, we obtain an analytic shape function that satisfies the geometric requirements for a traversable wormhole. The model parameter is constrained to $0<m<1/2$, corresponding to a quintessence-like regime with $-1<\omega<-1/3$. The energy conditions are analyzed in detail, showing that violations of the null and weak energy conditions are unavoidable but remain localized near the wormhole throat. The anisotropy parameter is positive throughout the spacetime, indicating that repulsive anisotropic stresses play a key role in sustaining the wormhole. The equilibrium configuration is examined using the generalized Tolman-Oppenheimer-Volkoff (TOV) equation for both zero and logarithmic redshift functions, where a consistent force balance is achieved with anisotropic effects providing the dominant outward support. Dynamical stability is studied through scalar perturbations, leading to a Schr\"odinger-like wave equation with a single-peak effective potential. The quasinormal modes are computed using the sixth-order WKB method with Pad\'e approximation. The resulting frequencies possess negative imaginary parts, indicating stable damping of perturbations. Time-domain simulations further confirm the stability of the solutions and show good agreement with the WKB results, with small deviations in the damping rates. Thus, these results establish that $f(Q)$ gravity admits traversable wormhole solutions that are geometrically consistent and dynamically stable, with $f(Q)$ gravity effects effectively regulating the required matter content.