Small nonspherical perturbations of the Choptuik spacetime decay, but large ones may grow

The Choptuik spacetime is the discretely self-similar, spherically symmetric critical solution that emerges at the threshold of black-hole formation in the gravitational collapse of a massless scalar field. Studying linear perturbations of this solution, Martin-Garcia and Gundlach found that all nonspherical perturbations decay. In an apparent contradiction, Choptuik et.al. found that some nonspherical deformations grew in their numerical simulations, ultimately leading to a bifurcation of the critical solution. I will report on new numerical simulations of the critical collapse of scalar fields in the absence of spherical symmetry. For small deviations from spherical symmetry, the deformations perform damped oscillations that are consistent with the findings of Martin-Garcia and Gundlach. For larger deviations, however, the deformations grow and form new centers of oscillations, consistent with the bifurcations observed by Choptuik et.al.. I speculate that this qualitative change in behavior is caused by nonlinear effects that lead to shifts in the parameters describing the critical solution and its deformations.