Dynamics of massive and massless particles in the spacetime of a wiggly cosmic dislocation

TL;DR

This work analyzes the dynamics of massive and massless particles in the spacetime of a wiggly cosmic dislocation, combining small-scale wiggles with spatial dislocation. By solving geodesic equations and the Klein-Gordon equation in the metric $ds^2 = -N(r)dt^2 + dr^2 + L(r)d\theta^2 + (\sqrt{M(r)}dz + \chi d\theta)^2$, the authors uncover a coupling between wiggles and dislocation that alters radial, angular, and axial motion. They show that the angular momentum is effectively modified to $m-k\chi$ and that the dispersion and bound-state spectra depend sensitively on $w$, $\chi$, and the propagation direction, with bound states arising from the combined potential $V_{\mathrm{eff}}(r)$. These findings elucidate how small-scale structure and topological defects jointly influence particle propagation and field dynamics in cosmic-string spacetimes, suggesting new avenues for cosmological modeling and wave propagation studies in defect-rich regions.

Abstract

In this paper, we investigate the spacetime containing both small-scale structures (wiggles) and spatial dislocation, forming a wiggly cosmic dislocation. We study the combined effects of these features on the dynamics of massive and massless particles. Our results show that while wiggles alone lead to bound states and dislocation introduces angular momentum corrections, their coupling produces more complex effects, influencing both particle motion and wave propagation. Notably, this coupling significantly modifies radial solutions and eigenvalues, with the direction of motion or propagation becoming a critical factor in determining the outcomes. Numerical solutions reveal detailed aspects of particle dynamics as functions of dislocation and string parameters, including plots of trajectories, radial probability densities, and energy levels. These findings deepen our understanding of how a wiggly cosmic dislocation shapes particle dynamics, suggesting new directions for theoretical exploration in cosmological models.

Figures (9)

• Figure 1: Orbits without dislocation: Figures (a) and (b) show no wiggles, while Figs. (c) and (d) illustrate their effects. Parameters in all figures are fixed at $Z=0.6$, $J=1.8$, $K=2$, and $\epsilon=-1$ (massive particles).
• Figure 2: Orbits under the effect of dislocation: Figure (a) shows the absence of wiggles but with dislocation, while Figs. (b) and (c) illustrates the presence of both wiggles and dislocation. We use the following parameters: $Z=0.6$, $J=1.8$, $K=2$, and $\epsilon=-1$.
• Figure 3: (a) The same as in Fig. \ref{['fig1']}(d). (b) The same as in Fig. \ref{['fig2']}(b). (c) The same as in Fig. \ref{['fig2']}(c). However, we use the fixed values $Z=-0.6$, $J=1.8$, $K=2$, and $\epsilon=-1$.
• Figure 4: (a) The same as in Fig. \ref{['fig2']}(b). (b) The same as in Fig. \ref{['fig2']}(c). (c) The same as in Fig. \ref{['fig3']}(b). (d) The same as in Fig. \ref{['fig3']}(c). However, here, we use $\epsilon=0$ (massless particles).
• Figure 5: Trivial orbits without dislocation (a) and with dislocation (b) for fixed values $Z=0.6$ and $J=1.8$. Figures (c) and (d) display the same comparison but for $Z=-0.6$ and $J=1.8$.