  We consider the nonlinear wave equation $i \partial_t u= \sqrt{-\Delta + m^2}
u - (|x|^{-1} \ast |u|^2) u$ on $\RR^3$ modelling the dynamics of
(pseudo-relativistic) boson stars. For spherically symmetric initial data,
$u_0(x) \in C^\infty_{\mathrm{c}}(\RR^3)$, with negative energy, we prove
blow-up of $u(t,x)$ in $H^{1/2}$-norm within a finite time. Physically, this
phenomenon describes the onset of "gravitational collapse" of a boson star. We
also study blow-up in external, spherically symmetric potentials and we
consider more general Hartree-type nonlinearities. As an application, we
exhibit instability for ground state solitary waves at rest if $m=0$.
