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We present a study of black hole threshold phenomena for a self-gravitating,massive complex scalar field in spherical symmetry. We construct Type Icritical solutions dynamically by tuning a one-parameter family of initial datacomposed of a boson star and a massless real scalar field. The real field isused to perturb the boson star via a gravitational interaction which results ina {\em significant} transfer of energy. The resulting critical solutions, whichshow great similarity with unstable boson stars, persist for a finite timebefore dispersing or forming a black hole. We extend the stability analysis ofGleiser and Watkins [Nucl. Phys. B319, 733 (1989)], providing a method forcalculating the radial dependence of boson star modes of nonzero frequency. Wefind good agreement between our critical solutions and boson star modes. Forcritical solutions less than 90% of the maximum boson star mass $M_{\rm max}\simeq 0.633 M_{Pl}^2/m$, a small halo of matter appears in the tail of thesolution. This halo appears to be an artifact of the collision between theoriginal boson star and the real field, and does not belong to the truecritical solution. It seems that unstable boson stars are unstable to dispersalin addition to black hole formation. Given the similarity in macroscopicstability between boson and neutron stars, we suggest that neutron stars at orbeyond the point of instability may also be unstable to explosion.Comment: 26 Pages, 16 Figures, RevTeX. Submitted to Phys. Rev.

Boson stars driven to the brink of black hole formation