Static traversable wormholes supported by a variable equation of state in f(Q, T) gravity

In this paper, we investigate static, spherically symmetric traversable wormholes in the framework of symmetric teleparallel f ( Q, T ) gravity by considering the linear model f ( Q , T ) = α Q + β T . By assuming a constant redshift function to describe zero tidal force geometries, we derive the corresponding field equations and obtain an analytic solution for the shape function by adopting a radially dependent equation of state of the form p r + ω ( r ) ρ = 0 , with ω ( r ) = A r n , where A > 0 and n > 0 are constants. The resulting wormhole configuration satisfies the fundamental geometric requirements, including the throat condition, the flare–out condition, and asymptotic flatness. The energy density remains positive and decreases with radius, while the null energy condition is violated only in the radial direction near the throat, indicating a localized exotic matter region. A Tolman–Oppenheimer–Volkoff analysis confirms that equilibrium is achieved through the balance between hydrostatic and anisotropic forces. Furthermore, the volume integral quantifier shows that the total amount of NEC–violating matter can be made arbitrarily small and confined close to the throat. The embedding diagrams support the geometric consistency of the solution. These results indicate that linear f ( Q, T ) gravity with a variable equation of state admits viable traversable wormhole solutions with minimized exotic matter content.

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