Boson stars driven to the brink of black hole formation

We present 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. The massless field is used to perturb the boson star via a purely gravitational interaction which results in a significant transfer of energy from the massless field to the massive field. The resulting (unstable) critical solutions, which display great similarity with unstable boson stars, persist for a finite time before either dispersing most of the mass to infinity (leaving a diffuse remnant) or forming a black hole. To further the comparison between our critical solutions and boson stars, we verify and extend the linear stability analysis of M. Gleiser and R. Watkins [Nucl. Phys. B319, 733 (1989)] by providing a method for calculating the radial dependence of boson star quasinormal modes of nonzero frequency. The frequencies observed in our critical solutions coincide with the mode frequencies obtained from perturbation theory, as do the radial profiles of many of the modes. For critical solutions with less than $90\%$ of the maximum boson star mass $M_{\max }\simeq {0.633M}_{\mathrm{Pl}}^2/m,$ the existence of a small halo of matter in the tail of the solution distorts the profiles which otherwise agree very well with unstable boson stars. These halos appear to be artifacts of the collision between the original boson star and the massless field, and do not appear to belong to the true critical solutions, which are interior to the halos and which do in fact correspond to unstable boson stars. It appears that unstable boson stars are unstable to dispersal (“explosion”) in addition to black hole formation, and given the similarities in macroscopic stability between boson stars and neutron stars, we suggest that those neutron star configurations at or beyond the point of instability may likewise be unstable to explosion.