Critical collapse of ultra-relativistic fluids: damping or growth of aspherical deformations

TL;DR

This study uses nonlinear simulations to analyze how aspherical perturbations evolve during ultra-relativistic fluid collapse, confirming theoretical predictions about damping, growth, and stability depending on the equation of state.

Contribution

It provides the first numerical confirmation of Gundlach's predictions regarding the behavior of aspherical modes in critical gravitational collapse.

Findings

Polar $ ext{l} = 2$ modes behave as predicted, with damping or growth depending on the equation of state.

Soft equations of state lead to damping, recovering spherical symmetry at criticality.

Stiff equations of state cause instability in $ ext{l} = 2$ modes, preventing power-law scaling.

Abstract

We perform fully nonlinear numerical simulations to study aspherical deformations of the critical self-similar solution in the gravitational collapse of ultra-relativistic fluids. Adopting a perturbative calculation, Gundlach predicted that these perturbations behave like damped or growing oscillations, with the frequency and damping (or growth) rates depending on the equation of state. We consider a number of different equations of state and degrees of asphericity and find very good agreement with the findings of Gundlach for polar $\ell = 2$ modes. For sufficiently soft equations of state, the modes are damped, meaning that, in the limit of perfect fine-tuning, the spherically symmetric critical solution is recovered. We find that the degree of asphericity has at most a small effect on the frequency and damping parameter, or on the critical exponents in the power-law scalings. Our findings also confirm, for the first time, Gundlach's prediction that the $\ell = 2$ modes become unstable for sufficiently stiff equations of state. In this regime the spherically symmetric self-similar solution can no longer be recovered by fine-tuning to the black-hole threshold, and one can no longer expect power-law scaling to hold to arbitrarily small scales.