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Stellar Collapse in the Time Dependent Hartree-Fock Approximation

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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 [3,4] 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.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, UAB, Birmingham, AL, 35294, USA

    Christian Hainzl

  2. Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333, Munich, Germany

    Benjamin Schlein

Authors
  1. Christian Hainzl
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  2. Benjamin Schlein
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Correspondence to Benjamin Schlein.

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Communicated by I. M. Sigal

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Hainzl, C., Schlein, B. Stellar Collapse in the Time Dependent Hartree-Fock Approximation. Commun. Math. Phys. 287, 705–717 (2009). https://doi.org/10.1007/s00220-008-0668-1

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  • DOI: https://doi.org/10.1007/s00220-008-0668-1

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