Stellar Collapse in the Time Dependent Hartree-Fock Approximation

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 Fröhlich 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.

13 pages

References in corpus (1)

• Blow-Up for Nonlinear Wave Equations describing Boson Stars

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• Many-Body Blow-Up Profile of Boson Stars with External Potentials
• Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
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• Blow-up profile of neutron stars in the Hartree-Fock-Bogoliubov theory