Exact solutions for slowly rotating wormholes in the presence of an anisotropic fluid

Abstract We construct slowly rotating traversable wormholes in the presence of an anisotropic fluid. Starting from a Teo-type stationary, axisymmetric extension of the Morris–Thorne metric, we perform a slow-rotation expansion, fix a gauge that preserves the geometric meaning of the radial coordinate, and introduce two complementary prescriptions for treating the throat (fixed and free). Within this framework, the Einstein equations and conservation laws form a closed system, from which we obtain analytic expressions for the leading frame dragging and for the second-order rotational backreaction. We apply the construction to the spatial–Schwarzschild and Morris–Thorne wormholes, derive the induced corrections to the stress–energy tensor, analyse the redistribution of null energy condition (NEC) violations, and characterise quadrupolar deformations, curvature diagnostics, and possible ergoregions.