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arXiv · 1805.10442

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

Juliana Celestino·Thomas W. Baumgarte
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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.

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Juliana Celestino, Thomas W. Baumgarte. 2018-05-26. Critical collapse of ultra-relativistic fluids: damping or growth of aspherical deformations. https://doi.org/10.1103/physrevd.98.024053

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