arXiv 0809.25602008-09math.APmath-phmath.MP

Minimizers for the Hartree-Fock-Bogoliubov Theory of Neutron Stars and White Dwarfs

Enno Lenzmann, Mathieu Lewin

备注：: 43 pages. Third and final version. Section 5 revised and main result extended. To appear in Duke Math. Journal.
发表信息：: Duke Math. J. 152, no. 2 (2010), 257-315
DOI：: 10.1215/00127094-2010-013

英文摘要：

We prove the existence of minimizers for Hartree-Fock-Bogoliubov (HFB) energy functionals with attractive two-body interactions given by Newtonian gravity. This class of HFB functionals serves as model problem for self-gravitating relativistic Fermi systems, which are found in neutron stars and white dwarfs. Furthermore, we derive some fundamental properties of HFB minimizers such as a decay estimate for the minimizing density. A decisive feature of the HFB model in gravitational physics is its failure of weak lower semicontinuity. This fact essentially complicates the analysis compared to the well-studied Hartree-Fock theories in atomic physics.

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