  We prove a general, non-perturbative result about finite-time blowup
solutions for the $L^2$-critical boson star equation $i\partial_t u =
\sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under
the sole assumption that the solution blows up in $H^{1/2}$ at finite time, we
show that $u(t)$ has a unique weak limit in $L^2$ and that $|u(t)|^2$ has a
unique weak limit in the sense of measures. Moreover, we prove that the
limiting measure exhibits minimal mass concentration. A central ingredient used
in the proof is a "finite speed of propagation" property, which puts a strong
rigidity on the blowup behavior of $u$.
  As the second main result, we prove that any radial finite-time blowup
solution $u$ converges strongly in $L^2$ away from the origin. For radial
solutions, this result establishes a large data blowup conjecture for the
$L^2$-critical boson star equation, similar to a conjecture which was
originally formulated by F. Merle and P. Raphael for the $L^2$-critical
nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704].
  We also discuss some extensions of our results to other $L^2$-critical
theories of gravitational collapse, in particular to critical Hartree-type
equations.
