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In this paper, we explore higher-dimensional asymptotically flat wormhole geometries in the framework of Gauss-Bonnet (GB) gravity and investigate the effects of the GB term, by considering a specific radial-dependent redshift function and by imposing a particular equation of state. This work is motivated by previous assumptions that wormhole solutions were not possible for the k=1 and <0 case, where k is the sectional curvature of an (n-2) -dimensional maximally symmetric space, and is the Gauss-Bonnet coupling constant. However, we emphasize that this discussion is purely based on a nontrivial assumption that is only valid at the wormhole throat, and cannot be extended to the entire radial-coordinate range. In this work, we provide a counterexample to this claim, and find for the first time specific solutions that satisfy the weak energy condition throughout the entire spacetime, for k=1 and <0. In addition to this, we also present other wormhole solutions which alleviate the violation of the weak energy condition in the vicinity of the wormhole throat.
Mehdizadeh et al. (Thu,) studied this question.