Oscillating kink behavior in a traversable wormhole

Abstract

We investigate the time evolution of spherically symmetric radial domain walls (kinks) in the background of a two-way traversable Simpson-Visser wormhole. By numerically solving the scalar-field equation with a double-well potential, we show that the wormhole throat parameter $a$ has a strong impact on the dynamics of the radial kink: larger $a$ leads to wider throats and allows the domain wall to oscillate across the throat with large amplitude, whereas smaller $a$ confines the motion nearby the throat. In addition, each time the kink crosses the wormhole throat, it emits scalar wave packets, causing its oscillation amplitude to gradually decrease. Our results reveal how the wormhole geometry influences the motion of defects and their energy transfer, providing new insights into the dynamics of topological defects in exotic spacetime.

Figures (6)

• Figure 1: The metric function $A(r)$ and the embedding function $z(\rho)$ with four different values of $a$, i.e., $a=15M$, $a=9M$, $a=6M$ and $a=2.02M$.
• Figure 2: Three-dimensional plot of rotations of the embedding function $z(\rho)$ along $\rho=0$, with panel (a) and panel (b) corresponding to $a=9M$ and $a=2.02M$, respectively.
• Figure 3: Time evolution of the scalar field $\phi$ in the wormhole background with four different values of $a$. In each panel, the scalar field shares the same initial configuration of the kink position at $r_k(0)=30$. Each panel is divided into two smaller parts, in which the solid line (in the upper part) represents the kink moving leftwards, while the dashed line (in the lower part) represents the kink moving rightwards. However, in the panel (d) we can see that in the lower part the dashed lines are confined nearby the throat of the wormhole. The black arrows in each panel represent the moving direction of the kinks.
• Figure 4: Time evolution of the kink's position $r_k(t)$ with four different values of the parameter $a$. In order to better illustrate the evolutions of the kink position, two dotted lines at $r_k=\pm30$ have been added as a reference.
• Figure 5: Configurations of the scalar field $\phi$ and its corresponding energy density $\mathcal{H}$ at different times, i.e., $t=5, 85$, and $151$. The initial position of the kink is $r_k(0)=30$, and the throat parameter is $a=9M$. The inset plots are the enlarged version of the wave packets or the energy densities as the arrows indicate.