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

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