PERTURBATIONS AND CRITICAL-BEHAVIOR IN THE SELF-SIMILAR GRAVITATIONALCOLLAPSE OF A MASSLESS SCALAR FIELD

This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar f ield (Roberts solution). The perturbation equations are derived and so lved exactly. The perturbation spectrum is found to be not discrete, b ut occupying a continuous region of the complex plane. The renormaliza tion group calculation gives the value of the mass-scaling exponent be ta = 1. [S0556-2821(97)02422-3].