Critical Behavior in Gravitational Collapse of Radiation Fluid: A Renormalization Group (Linear Perturbation) Analysis

A scenario is presented, based on renormalization group (linear perturbation) ideas, which can explain the universality and scaling observed in a numerical study of gravitational collapse of radiation fluid. In particular, it is shown that the critical exponent β and the largest Lyapunov exponent Reκ of the perturbation is related by β0ex0ex=0ex0ex(Reκ)^-1. We find the relevant perturbation mode numerically, and obtain a fairly accurate value of the critical exponent β0.35580192, also in agreement with that obtained in numerical simulation.