Duke Mathematical Journal

Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs

Enno Lenzmann and Mathieu Lewin

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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 a 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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Duke Math. J. Volume 152, Number 2 (2010), 257-315.

First available in Project Euclid: 31 March 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20]


Lenzmann, Enno; Lewin, Mathieu. Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs. Duke Math. J. 152 (2010), no. 2, 257--315. doi:10.1215/00127094-2010-013. https://projecteuclid.org/euclid.dmj/1270041109.

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