Aspherical deformations of the Choptuik spacetime

TL;DR

This paper investigates how deviations from spherical symmetry affect critical phenomena in gravitational collapse, revealing stability for small deviations and instability leading to bifurcations for larger ones, through numerical simulations.

Contribution

It provides the first detailed numerical analysis of non-spherical perturbations in critical gravitational collapse, showing nonlinear effects alter critical parameters and induce bifurcations.

Findings

Small deviations behave like damped oscillations consistent with linear theory.

Increasing deviations decrease critical exponent and echoing period.

Large deviations lead to unstable growth and bifurcation with multiple collapse centers.

Abstract

We perform dynamical and nonlinear numerical simulations to study critical phenomena in the gravitational collapse of massless scalar fields in the absence of spherical symmetry. We evolve axisymmetric sets of initial data and examine the effects of deviation from spherical symmetry. For small deviations we find values for the critical exponent and echoing period of the discretely self-similar critical solution that agree well with established values; moreover we find that such small deformations behave like damped oscillations whose damping coefficient and oscillation frequencies are consistent with those predicted in the linear perturbation calculations of Martin-Garcia and Gundlach. However, we also find that the critical exponent and echoing period appear to decrease with increasing departure from sphericity, and that, for sufficiently large departures from spherical symmetry, the deviations become unstable and grow, confirming earlier results by Choptuik et.al.. We find some evidence that these growing modes lead to a bifurcation, similar to those reported by Choptuik et.al., with two centers of collapse forming on the symmetry axis above and below the origin. These findings suggest that nonlinear perturbations of the critical solution lead to changes in the effective values of the critical exponent, echoing period and damping coefficient, and may even change the sign of the latter, so that perturbations that are stable in the linear regime can become unstable in the nonlinear regime.