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 $\beta$ and the largest Lyapunov exponent $\mathrm{Re}\kappa$ of the perturbation is related by $\beta =(\mathrm{Re}\kappa {)}^{-1}$. 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.

4 pages in ReVTeX, 2 uuencoded eps figures, uses BoxedEPSF.tex

References in corpus (1)

• Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid

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