  We present a brief synopsis of related work (gr-qc/0007039), describing a
study of black hole threshold phenomena for a self-gravitating, massive complex
scalar field in spherical symmetry. We construct Type I critical solutions
dynamically by tuning a one-parameter family of initial data consisting of a
boson star and a massless real scalar field, and numerically evolving this
data. The resulting critical solutions appear to correspond to boson stars on
the unstable branch, as we show via comparisons between our simulations and
perturbation theory. For low-mass critical solutions, we find small ``halos''
of matter in the tails of the solutions, and these distort the profiles which
otherwise agree with unstable boson stars. These halos seem to be artifacts of
the collisions between the original boson stars and the massless fields, and do
not appear to belong to the true critical solutions. From this study, it
appears that unstable boson stars are unstable to dispersal (``explosion'') in
addition to black hole formation. Given the similarities in macroscopic
stability between boson stars and neutron stars, we suggest that similar
phenomena could occur in models of neutron stars.
