Dynamics of $U(1)$ gauged Q-balls in three spatial dimensions

We investigate the dynamics of $U(1)$ gauged Q-balls using fully three-dimensional numerical simulations. We consider two different scenarios: first, the classical stability of gauged Q-balls with respect to generic three-dimensional perturbations, and second, the behaviour of gauged Q-balls during head-on and off-axis collisions at relativistic velocities. With regard to stability, we find that there exist gauged Q-ball configurations which are classically stable in both logarithmic and polynomial scalar field models. With regard to relativistic collisions, we find that the dynamics can depend on many different parameters such as the collision velocity, relative phase, relative charge, and impact parameter of the colliding Q-balls.