Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity

The solutions of traversable wormholes and their geometries are investigated in higher-curvature gravity with boundary terms for each case under the presence of anisotropic, isotropic and barotropic fluids in detail. For each case, the effective energy-momentum tensor violates the null energy condition throughout the wormhole throat. The null and weak energy conditions are also analyzed for ordinary matters. The regions that physically viable wormhole solutions can exist are explicitly shown. Furthermore, it is found that the range of the viable regions exhibits an alternating pattern of expansion and contraction. The present analyses can reveal the regions in which traversable wormholes can be constructed for anisotropic, isotropic and barotropic fluids cases with incorporating realistic matter contents, leading to fundamental physics insights into the feasible construction of wormholes in higher-curvature gravity with boundary term. The main achievements of this work, in contrast to previous studies, are its thorough investigation of traversable wormholes within the framework of higher-curvature gravity with boundary terms, its extensive consideration of various fluid types, and the explicit identification of regions where stable wormhole solutions can exist.