Critical phenomena in perfect fluids

TL;DR

This paper studies the gravitational collapse of perfect fluids with different equations of state, identifying unique critical solutions and their properties, including self-similarity and mass-scaling behavior, through numerical and analytical methods.

Contribution

It extends the understanding of critical phenomena in gravitational collapse for perfect fluids, confirming the existence of unique critical solutions across a range of gamma values and analyzing their characteristics.

Findings

Existence of locally unique critical solutions for 1.05 < Gamma < 1.89.

Evidence for globally regular critical solutions for 1.89 < Gamma <= 2.

Mass-scaling exponents consistent with linear perturbation theory.

Abstract

We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black hole formation is anticipated to turn on at infinitesimal black hole mass (Type II behavior). Critical solutions (those which sit at the threshold of black hole formation in parametrized families of collapse) are found by solving the system of ODEs which result from a self-similar ansatz, and by solving the full Einstein/fluid PDEs in spherical symmetry. These latter PDE solutions (``simulations'') extend the pioneering work of Evans and Coleman (Gamma = 4/3) and verify that the continuously self-similar solutions previously found by Maison and Hara et al for $1.05 < Gamma < 1.89 are (locally) unique critical solutions. In addition, we find strong evidence that globally regular critical solutions do exist for 1.89 < Gamma <= 2$, that the sonic point for Gamma_dn = 1.8896244 is a degenerate node, and that the sonic points for Gamma >Gamma_dn are nodal points rather than focal points as previously reported. We also find a critical solution for Gamma = 2, and present evidence that it is continuously self-similar and Type II. Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory. Finally, we comment on critical solutions generated with an ideal-gas equation of state.