Semiclassical Equivalence of Two White Dwarf Models as Ground States of the Relativistic Hartree–Fock and Vlasov–Poisson energies

We are concerned with the semi-classical limit for ground states of the relativistic Hartree–Fock energies (HF) under a mass constraint, which are considered as the quantum mean-field model of white dwarfs (Lenzmann and Lewin in Duke Math J 152:257–315, 2010). In Jang and Seok (Kinet Relat Models 15:605–620, 2022), fermionic ground states of the relativistic Vlasov–Poisson energy (VP) are constructed as a classical mean-field model of white dwarfs, and are shown to be equivalent to the classical Chandrasekhar model. In this paper, we prove that as the reduced Planck constant \(\hbar \) goes to the zero, the \(\hbar \)-parameter family of the ground energies and states of (HF) converges to the fermionic ground energy and state of (VP) with the same mass constraint.