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

Gareth Arturo Marks

TL;DR

This work investigates the nonlinear radial stability of boson stars with a solitonic potential, including ultracompact configurations on the perturbatively stable branch. The authors evolve self-gravitating complex scalar fields under explicit perturbations using a dimensional reduction of CCZ4/BSSN, while tracking the Noether charge and binding energy $E_B = M - mu N$. They find robust nonlinear radial stability for perturbatively stable models with $E_B>0$, challenging the common belief that negative binding energy is required for dynamical stability, and observe that some stable configurations do not disperse under perturbations. The results suggest an obstruction to complete dispersion arising from the solitonic potential and motivate extending the analysis beyond spherical symmetry and across broader scalar potentials.

Abstract

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.

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

TL;DR

This work investigates the nonlinear radial stability of boson stars with a solitonic potential, including ultracompact configurations on the perturbatively stable branch. The authors evolve self-gravitating complex scalar fields under explicit perturbations using a dimensional reduction of CCZ4/BSSN, while tracking the Noether charge and binding energy . They find robust nonlinear radial stability for perturbatively stable models with , challenging the common belief that negative binding energy is required for dynamical stability, and observe that some stable configurations do not disperse under perturbations. The results suggest an obstruction to complete dispersion arising from the solitonic potential and motivate extending the analysis beyond spherical symmetry and across broader scalar potentials.

Abstract

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.

Paper Structure

This paper contains 4 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory and Numerical Setup
  3. Results and Discussion
  4. Conclusions

Figures (2)

  • Figure 1: The ADM mass $M$ (left) and binding energy $E_B$ (right) against the central scalar-field amplitude $A_0$ for families of BS solutions with varying parameter $\sigma_0$. Solid lines indicate perturbative stability, while dashed indicate instability; see e.g. Ref. Marks:2025 for details. The inset draws attention to the region in which linearly stable models with positive binding energy exist.
  • Figure 2: Power spectrum of the central amplitude oscillations for evolution B1, showing peaks at the fundamental frequency $\chi_0$ and first excited frequency $\chi_1$, represented by vertical lines. The inset displays $A_0$ in the time domain for reference.