Blow-up Profile of Neutron Stars in the Chandrasekhar theory

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.