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arXiv · 0809.2560

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

Enno Lenzmann·Mathieu Lewin
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Abstract

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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Enno Lenzmann, Mathieu Lewin. 2008-09-15. Minimizers for the Hartree-Fock-Bogoliubov Theory of Neutron Stars and White Dwarfs. https://doi.org/10.1215/00127094-2010-013

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