The wiggly cosmic string as a waveguide for massless and massive fields

We examine the effect of a wiggly cosmic string for both massless and massive particle propagation along the string axis. We show that the wave equation that governs the propagation of a scalar field in the neighborhood of a wiggly string is formally equivalent to the quantum wave equation describing the hydrogen atom in two dimensions. We further show that the wiggly string spacetime behaves as a gravitational waveguide in which the quantized wave modes propagate with frequencies that depend on the mass, string energy density, and string tension. We propose an analogy with an optical fiber, defining an effective refractive index likely to mimic the cosmic string effect in the laboratory.