What the study found
The study found that self-gravitating bosonic configurations have equilibrium and stability limits in the nonrelativistic regime. The authors identify a critical central density and a maximum particle number, and they note that excited configurations that satisfy the virial relation are expected to be metastable.
Why the authors say this matters
The authors conclude that the critical particle number can be used to estimate the maximum stable mass and radius of these configurations. For axion-like bosons, the study suggests masses of tens of Earth masses and radii on the order of meters.
What the researchers tested
The researchers numerically solved the nonlinear Gross–Pitaevskii–Poisson equations, which describe a bosonic quantum fluid coupled to gravity, in the nonrelativistic regime. They used a coordinate transformation to write the equations in dimensionless form and then computed sequences of stationary solutions, including ground states and radially excited states.
What worked and what didn't
The analysis identified bifurcation points between ground and radially excited states. The virial relation worked as a diagnostic for equilibrium and led to the determination of a critical central density and maximum particle number. Stationary solutions were not found above that particle-number limit, and the excited configurations were described as expected to be metastable because they violate stability conditions from radial perturbation analyses.
What to keep in mind
The abstract describes only the nonrelativistic regime, so the results are limited to that setting. It also does not provide detailed numerical values for the critical density or particle number in the summary, beyond the axion-like boson example.
Key points
- A critical central density and maximum particle number were identified for self-gravitating bosonic configurations.
- No stationary solutions were found above the maximum particle-number limit.
- Ground states and radially excited states were both computed, with bifurcation points identified between them.
- Excited configurations satisfying the virial relation were expected to be metastable.
- For axion-like bosons with mass 10−5 eV, the configurations were estimated to have tens of Earth masses and meter-scale radii.
Disclosure
- Research title:
- Self-gravitating bosonic configurations show critical stability limits
- Authors:
- Gilbert Reinisch, J. A. de Freitas Pacheco
- Institutions:
- Observatoire de la Côte d’Azur, Observatoire de la Côte d’Azur
- Publication date:
- 2026-04-03
- OpenAlex record:
- View
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