Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---

Abstract

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 $β$ and the largest Lyapunov exponent ${\rm Re\, } κ$ of the perturbation is related by $β= ({\rm Re\, } κ) ^{-1}$. We find the relevant perturbation mode numerically, and obtain a fairly accurate value of the critical exponent $β\simeq 0.3558019$, also in agreement with that obtained in numerical simulation.