Scalar-Wave Signatures of Wormholes in Dark Matter Halos

TL;DR

The paper develops an exact, non-perturbative framework to study massless scalar-wave propagation in static, spherically symmetric wormholes embedded in realistic dark matter halos by deriving a generalized Helmholtz equation with a position- and frequency-dependent effective refractive index $n_eff(r,omega)$ that separates contributions from gravitational redshift, curvature, and angular momentum. It analyzes representative halo models (NFW, TF/BEC, PI) and redshift prescriptions (zero, Teo, cored), revealing evanescent regions and angular-momentum–dependent mode suppression near the throat, with a clear wave–geodesic correspondence in the geometric-optics limit. The work shows how photon spheres and shadows depend on the redshift profile, producing an observable shadow only for Teo-type redshifts, while zero-redshift and cored profiles are shadowless; it also connects the framework to transformation optics and discusses observational and laboratory analogues. Overall, the results provide a robust, non-perturbative tool to predict scalar-wave signatures of halo-embedded wormholes and to guide potential multi-messenger probes and metamaterial simulations.

Abstract

We identify scalar-wave signatures of massless fields propagating in static, spherically symmetric wormholes embedded within realistic dark matter halos. Starting from a general line element with arbitrary redshift and shape functions, we recast the radial Klein-Gordon equation in Schrödinger form, explicitly separating contributions from 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 the throat geometry, halo curvature, and centrifugal effects, asymptotically recovering free-space propagation. Applying this framework to Navarro-Frenk-White, Thomas-Fermi Bose-Einstein condensate, and Pseudo-Isothermal halo models, and considering zero, Teo-type, and cored redshift functions, we uncover evanescent regions and suppression of high-angular-momentum modes in the vicinity of the throat. High-frequency waves approach the geometric-optics regime, whereas low-frequency modes exhibit strong curvature-induced localization. In the geometric-optics limit, the effective refractive index reproduces null-geodesic trajectories, while finite-frequency effects capture evanescent zones and tunneling phenomena. This work establishes the first exact, non-perturbative framework linking wormhole geometry and realistic dark matter halos to observable scalar-wave propagation phenomena, including evanescence, mode suppression, and frequency-dependent localization.

Figures (1)

• Figure 1: Effective refractive index squared $n_\mathrm{eff}^2(\omega,r)$ for various wormhole and halo models as a function of the radial coordinate $r$. The rows correspond to different halo profiles: (i) NFW Halo, (ii) TF (BEC) Halo, and (iii) PI Halo. The columns represent different frequencies $\omega = 0.5, 0.9, 1.3$. Redshift functions considered are: Zero redshift $\Phi(r) = 0$, Teo redshift $\Phi(r) = -a/r$ with $a = 0.5$, and Cored redshift $\Phi(r) = \ln\left[ 1 + A / (1 + (r/r_0)^{n_\mathrm{Core}} ) \right]$ with $A = 0.5$, $r_0 = 1.0$ and $n_\mathrm{Core} = 2$. Shape functions for the halos are parametrized using $\rho_s = 0.01$, $R_s = 1.0$, and $\epsilon_0 = 0.1$. Shaded gray regions indicate evanescent zones where $n_\mathrm{eff}^2 < 0$, corresponding to classically forbidden regions with exponential wave decay. The black dashed line marks $n_\mathrm{eff}^2 = 0$.