A static spherically symmetric thin shell wormhole colliding with a spherical thin shell

TL;DR

This paper analyzes the dynamics of a static spherically symmetric thin shell wormhole colliding with a matter shell, revealing conditions for bouncing or passing through, with implications for wormhole stability and evolution.

Contribution

It provides a new analytical framework for understanding thin shell wormhole collisions using geometrical constraints and conservation laws.

Findings

Shell may bounce back or pass through the wormhole.

Wormhole shrinks after collision in both cases.

Radial speeds follow an addition law in the bouncing case.

Abstract

We consider a static spherically symmetric thin shell wormhole collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the "bouncing" case, a surprising result is that the radial speeds before and after the collision satisfy an addition law, which is independent of the masses of the wormhole and the shell. Once the shell passes through the wormhole, we find that the shell always expands. However, the expansion rate is the same as its collapsing rate right before the collision. Finally, we find out the solution for the shell moving together with the wormhole.