Slowly Rotating Traversable Wormholes Supported by Radially Varying String‐Fluid Matter: From Regular Geometries to Photon Trajectories

ABSTRACT This work investigates slowly rotating traversable wormholes supported by string fluids whose properties vary with distance from the throat. This radial variation allows the matter to transition smoothly from a de Sitter‐like core near the center to a string‐dominated environment further out, producing a regular, horizon‐free, and asymptotically flat spacetime. By allowing the transverse pressure to depend on radius, the fluid adapts naturally to the surrounding geometry, yielding a well‐behaved energy density and shape function. Even modest rotation introduces frame‐dragging effects that twist photon paths, creating differences between co‐rotating and counter‐rotating trajectories. These effects are strongest near the throat, while at larger distances the spacetime is largely governed by the static gravitational field. Circular photon orbits reveal that the interplay of the redshift function, wormhole shape, and rotation determines the photon‐sphere structure. Different radial profiles of the string fluid generate distinctive photon‐ring patterns, providing potential observational signatures of both rotation and the internal matter distribution. Overall, radially varying string fluids provide a flexible and physically consistent source for traversable wormholes, bridging vacuum‐like and string‐dominated regions while maintaining regularity and supporting slow‐rotation. This study highlights how anisotropic matter influences curvature and light propagation, offering a realistic framework for horizonless exotic spacetimes.