Stability of Self-Gravitating Bosonic Configurations

Key findings from this study

This research indicates that:

• A critical particle number above which no stationary solutions exist can be determined from the virial relation, establishing an upper bound on stable configuration mass and radius.
• Excited configurations satisfying equilibrium conditions are metastable because they violate stability criteria from radial perturbation analysis.
• For axion-like bosons at 10^−5 eV, predicted stable configurations span tens of Earth masses with meter-scale radii.

Overview

Numerical investigation of equilibrium and stability properties for self-gravitating bosonic systems in the nonrelativistic regime. The analysis solves the coupled Gross–Pitaevskii–Poisson equations using dimensionless coordinate transformations to identify bifurcations between ground and excited stationary states. The virial relation determines equilibrium conditions and identifies critical thresholds beyond which stationary solutions cease to exist.

Methods and approach

The authors solved the nonlinear Gross–Pitaevskii–Poisson system numerically using coordinate transformations that render the equations independent of physical parameters. Each configuration is uniquely determined by the central wave function value. Sequences of stationary solutions spanning ground and radially excited states were computed and analyzed for bifurcation points. Stability was assessed through radial perturbation analysis, while the virial relation served as equilibrium diagnostic.

Results

Numerical solutions establish a critical central density and maximum particle number above which stationary configurations vanish. The virial relation identifies metastable excited states that violate stability conditions derived from perturbation analyses. From the critical particle number threshold, maximum stable mass and radius estimates were derived. For axion-like bosons with mass 10^−5 eV, the resulting configurations exhibit masses of tens of Earth masses with meter-scale radii.

Implications

The stability analysis provides constraints on self-gravitating bosonic systems relevant to theoretical models of dark matter and ultralight bosonic candidates. The critical density and particle number thresholds establish bounds on viable equilibrium configurations in the nonrelativistic regime. The computed mass-radius relations for axion-like bosons offer predictions for observational signatures in compact object searches and gravitational wave detection.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.