# Blow-up profile of neutron stars in the Hartree-Fock-Bogoliubov theory

## TL;DR

This paper analyzes the gravitational collapse of neutron stars within the Hartree-Fock-Bogoliubov framework, showing that as particle number grows, the star's profile converges to a universal Lane-Emden solution near the Chandrasekhar limit.

## Contribution

It establishes the universal blow-up profile of neutron stars in the Hartree-Fock-Bogoliubov theory approaching the Chandrasekhar limit.

## Key findings

- Minimizers develop a universal blow-up profile
- Profile converges to Lane-Emden solution
- Results hold as particle number becomes large and gravity weakens

## Abstract

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.