Phases of massive scalar field collapse

Abstract

We study critical behavior in the collapse of massive spherically symmetric scalar fields. We observe two distinct types of phase transition at the threshold of black hole formation. Type II phase transitions occur when the radial extent $(\ensuremath{\lambda})$ of the initial pulse is less than the Compton wavelength $({\ensuremath{\mu}}^{\ensuremath{-}1})$ of the scalar field. The critical solution is that found by Choptuik in the collapse of massless scalar fields. Type I phase transitions, where the black hole formation turns on at finite mass, occur when $\ensuremath{\lambda}\ensuremath{\mu}\ensuremath{\gg}1$. The critical solutions are unstable soliton stars with masses $\ensuremath{\lesssim}0.6{\ensuremath{\mu}}^{\ensuremath{-}1}$. Our results in combination with those obtained for the collapse of a Yang-Mills field [M. W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996)] suggest that unstable, confined solutions to the Einstein-matter equations may be relevant to the critical point of other matter models.