Critical behaviour 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 self-similarity and scaling observed in a numerical study of gravitational collapse of radiation fluid. In particular, it is shown that the critical exponent \beta and the largest Lyapunov exponent {\rm Re\, } \kappa of the perturbation is related by \beta= ({\rm Re\, } \kappa) ^{-1}. We find the relevant perturbation mode numerically, and obtain a fairly accurate value of the critical exponent \beta \simeq 0.3558019, also in agreement with that obtained in numerical simulation