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

TL;DR

This paper proves the existence of minimizers for Hartree-Fock-Bogoliubov energy functionals modeling self-gravitating neutron stars and white dwarfs, addressing mathematical challenges due to gravitational interactions.

Contribution

It establishes the existence of minimizers for gravitational HFB functionals and analyzes their properties, advancing the mathematical understanding of astrophysical Fermi systems.

Findings

Existence of minimizers proven for gravitational HFB functionals

Decay estimates derived for minimizing densities

Analysis addresses non-lower semicontinuity challenges

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.