  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.
