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

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.

11 pages, 8 figures; see also http://www.bowdoin.edu/~tbaumgar/rad_fluid_movie.mp4 for an animation

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• Simulations of Ellipsoidal Primordial Black Hole Formation
• Effective inspiral spin distribution of primordial black hole binaries
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Critical phenomena in gravitational collapse of Husain-Martinez-Nunez scalar field