English

Self-gravitating Bose-Einstein condensates and the Thomas-Fermi approximation

General Relativity and Quantum Cosmology 2016-08-16 v3 Astrophysics of Galaxies Quantum Gases

Abstract

Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet it is well known that this assumption is violated near the condensate surface. We also show that the total energy of the self-gravitating condensate in the TF-approximation is positive. The stability of a self-gravitating system is dependent on the total energy being negative. Therefore, the TF-approximation is ill suited to formulate initial conditions in numerical simulations. As an alternative, we offer an approximate solution of the full GPP system.

Keywords

Cite

@article{arxiv.1402.0600,
  title  = {Self-gravitating Bose-Einstein condensates and the Thomas-Fermi approximation},
  author = {Viktor T. Toth},
  journal= {arXiv preprint arXiv:1402.0600},
  year   = {2016}
}

Comments

8 pages, 2 figures. Updated manuscript to match published version

R2 v1 2026-06-22T03:00:30.281Z