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

TY - JOUR

T1 - Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs

AU - Lenzmann, Ralf-Enno

AU - Lewin, Mathieu

PY - 2010/4

Y1 - 2010/4

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0012-7094

VL - 152

SP - 257

EP - 315

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 2

ER -