More recently, Choptuik and collaborators  have carried out axisymmetric time evolutions for the massless scalar field using adaptive mesh refinement. They find that in the limit of fine-tuning generic axisymmetric initial data the spherically symmetric critical solution is approached at first but then deviates from spherical symmetry and eventually develops two centres, each of which approaches the critical solution and bifurcates again in a universal way. This suggests that the critical solution has non-spherical growing perturbation modes, possibly a single l = 2 even parity mode (in axisymmetry, only m = 0 is allowed). There appears to be a conflict between the time evolution results  and the perturbative results , which needs to be resolved by more work (see Section 5.2).
Perturbing the scalar field around spherical symmetry, angular momentum comes in to second order in perturbation theory. All angular momentum perturbations were found to decay, and a critical exponent for the angular momentum was derived for the massless scalar field in . This prediction has not yet been tested in nonlinear collapse simulations.
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