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

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.

43 pages. Third and final version. Section 5 revised and main result extended. To appear in Duke Math. Journal.

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• Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
• Hartree-Fock theory for pseudorelativistic atoms
• Stellar Collapse in the Time Dependent Hartree-Fock Approximation

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