We study the dynamics of $U(1)$ gauged $Q$-balls using fully nonlinear numerical evolutions in axisymmetry. Focusing on two models with logarithmic and polynomial scalar field potentials, we numerically evolve perturbed gauged $Q$-ball configurations in order to assess their stability and determine the fate of unstable configurations. Our simulations suggest that there exist both stable and unstable branches of solutions with respect to axisymmetric perturbations. For solutions belonging to the stable branch, the gauged $Q$-balls respond to the perturbations by oscillating continuously or weakly radiating before returning to the initial configuration. For the unstable branch, the solutions are eventually destroyed and can evolve in several ways, such as dispersal of the fields to infinity or fragmentation into smaller gauged $Q$-balls. In some cases, we observe the formation of ringlike structures which we call “gauged $Q$-rings.” We also investigate the stability of gauged $Q$-balls when the gauge coupling is small, finding that the behavior of these configurations closely resembles that of ordinary (nongauged) $Q$-balls.

• Received 22 November 2022
• Accepted 10 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.035022

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Published by the American Physical Society