Blow-up profile of neutron stars in the Hartree–Fock–Bogoliubov theory
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We consider the gravitational collapse for neutron stars in the Hartree–Fock–Bogoliubov theory. We prove that when the number particle becomes large and the gravitational constant is small such that the attractive interaction strength approaches the Chandrasekhar limit mass slowly, the minimizers develop a universal blow-up profile. It is given by the Lane–Emden solution.
Mathematics Subject Classification81V17 35Q55 49J40
The manuscript was completed when the author was visiting the Mittag–Leffler Institute for the semester program Spectral Methods in Mathematical Physics. The author would like to thank the organizers for their warm hospitality. He also thanks E. Lenzmann for helpful comments. The research received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868.
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