Stellar Collapse in the Time Dependent Hartree-Fock Approximation

TL;DR

This paper proves finite-time blow-up for radially symmetric solutions of the pseudo-relativistic Hartree-Fock equation with negative energy, advancing understanding of white dwarf dynamics.

Contribution

It extends previous blow-up results to the Hartree-Fock model, incorporating the exchange term via angular momentum conservation.

Findings

Finite-time blow-up for solutions with negative energy

Extension of blow-up results to Hartree-Fock equations

Use of angular momentum conservation to handle exchange term

Abstract

We prove blow-up in finite time for radially symmetric solutions to the pseudo-relativistic Hartree-Fock equation with negative energy. The non-linear Hartree-Fock equation is commonly used in the physics literature to describe the dynamics of white dwarfs. We extend thereby recent results by Fr\"ohlich and Lenzmann, who established in \cite{FL1,FL2} blow-up for solutions to the pseudo-relativistic Hartree equation. As key ingredient for handling the exchange term we use the conservation of the expectation of the square of the angular momentum operator.