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

TL;DR

This paper uses renormalization group analysis to explain the self-similarity and scaling in gravitational collapse of radiation fluid, accurately predicting the critical exponent and perturbation modes consistent with numerical simulations.

Contribution

It introduces a renormalization group framework to analytically understand critical phenomena in gravitational collapse, linking perturbation modes to observed scaling.

Findings

Critical exponent approximately 0.356 consistent with simulations

Perturbation mode identified numerically

Relation between Lyapunov exponent and critical exponent established

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 $\beta$ 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.