Blow-up Profile of Neutron Stars in the Chandrasekhar theory

TL;DR

This paper analyzes the Chandrasekhar model for neutron stars, establishing the existence of minimizers below a critical interaction strength and describing their blow-up behavior as this threshold is approached.

Contribution

It proves the existence of minimizers for the model below the Chandrasekhar limit and characterizes the blow-up profile as a Lane-Emden solution.

Findings

Existence of minimizers for interaction strength below the Chandrasekhar limit.

Blow-up profile of minimizers converges to Lane-Emden solution.

Behavior of neutron star models near critical interaction strength.

Abstract

We study the Chandrasekhar variational model for neutron stars, with or without an external potential. We prove the existence of minimizers when the attractive interaction strength $\tau$ is strictly smaller than the Chandrasekhar limit $\tau_c$ and investigate the blow-up phenomenon in the limit $\tau\uparrow \tau_{c}$. We show that the blow-up profile of the minimizer(s) is given by the Lane-Emden solution.