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Abstract

We develop an exact analytic framework for massless scalar-wave propagation in static, spherically symmetric wormholes embedded in realistic dark matter halos. Starting from a general line element with arbitrary redshift and shape functions, we derive the radial Klein-Gordon equation in Schr\"odinger form, disentangling the effects of gravitational redshift, spatial curvature, and angular momentum. The dynamics reduce to a generalized Helmholtz equation with a space- and frequency-dependent effective refractive index that encodes throat geometry, halo curvature, and centrifugal contributions. In the asymptotic limit $r \to \infty$, the refractive index approaches unity, consistently recovering free-space propagation. Application to representative halo profiles, including the Navarro-Frenk-White model, the Thomas-Fermi Bose-Einstein condensate, and the Pseudo-Isothermal distribution, combined with zero, Teo-type, and cored redshift functions, reveals evanescent domains, quasi-bound states, and suppression of high-angular-momentum modes near the throat. High-frequency waves converge to the geometric-optics regime, whereas low-frequency modes undergo strong curvature-induced localization. This formalism establishes a non-perturbative link between wormhole geometry, halo structure, and redshift effects, providing a robust framework for scalar-wave phenomenology in astrophysical contexts.