FINE-STRUCTURE OF CHOPTUIKS MASS-SCALING RELATION

We conjecture (analytically) and demonstrate (numerically) the existen ce of a fine structure above the power-law behavior of the mass of bla ck holes that form in the gravitational collapse of a spherical massle ss scalar field. The fine structure is a periodic function of the crit ical separation (p-p). We predict that the period <(omega)over bar> i s universal and that it depends on the previous universal parameters, the critical exponent beta, and the echoing period Delta as <(omega)ov er bar> = Delta/(2 beta).