Perturbations of Solitonic Boson Stars: Nonlinear Radial Stability and Binding Energy

We study the nonlinear radial stability of boson stars with a solitonic potential across the entire parameter space, focusing especially on families of solutions that support ultracompact models on the perturbatively stable branch. Using a dimensional reduction of the CCZ4 formulation of numerical relativity, we dynamically evolve these models with both internal and external perturbations. We find in particular that there are perturbatively stable models with positive binding energy that do not effectively disperse even under explicit perturbations, challenging the conventional wisdom that negative binding energy is a necessary condition for the dynamical stability of boson stars and other compact objects.

💡 Research Summary

This paper investigates the nonlinear radial stability of boson stars (BSs) constructed with a solitonic self‑interaction potential, covering the full range of model parameters. The authors focus especially on configurations that lie on the perturbatively stable branch yet possess ultracompact (UCO) properties, i.e., they are compact enough to support a pair of light rings (one stable, one unstable). Using a dimensional reduction of the CCZ4 formulation of numerical relativity, they evolve these spherically symmetric models under both internal and external perturbations.

The theoretical setup starts from a minimally coupled complex scalar field φ with the solitonic potential
(V(\phi)=\mu^{2}|\phi|^{2}\bigl