Analytic example of critical behaviour in scalar field collapse

An exact one parameter () family of solutions representing scalar field collapse is shown to exhibit a type of critical behaviour which has been discussed by Choptuik. The three possible evolutions are outlined. For supercritical evolution (when black holes form) it is shown that a quantity related to the mass of the black hole exhibits a power law dependence on , for near critical evolution . The solution supports the conjecture that black hole formation initially occurs at infinitesimal mass.