Wiggly cosmic string as a waveguide for massless and massive fields

Abstract

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.

Two- and Three-Particle Complexes with Logarithmic Interaction: Compact Wave Functions for Two-Dimensional Excitons and Trions

“…Interestingly, the same spectral problem defined by equation ( 5) can appear in another context. Indeed, the effect of a wiggly cosmic string for both mass-less and massive particle propagation along the string axis is governed by (5), see [26].…”

“…to remove in (26) the appearance of physical constants (except for the masses m 1 and m 2 = m 3 ). Therefore, the trion ground state wavefunction corresponds to the nodeless solution of the equation…”

Classical Kalb-Ramond field theory in curved spacetimes

“…The Kalb-Ramond fields can be obtained via tensor calculus (30) and (33), via ordinary vector formalism (37), ( 38) and ( 39), but in order to illustrate the power of exterior differential calculus, we will consider the static Kalb-Ramond field created by a localized source distribution in various spacetimes, assimilated to fixed backgrounds, using mainly Eqs. ( 21) and (24).…”

“…In the weak gravitational field approximation, the linearized line element in the presence of a wiggly string oriented along the z-axis is given by [30][31][32][33]:…”