Completely parallel results can be found for wave maps, for which the critical dimension is 2+1. For the wave map from 3+1 Minkowski to the 3-sphere, Bizoń  has shown that there is a countable family of regular (before the CH) CSS solutions labeled by a nodal number , such that each solution has n unstable modes. Simulations of collapse in spherical symmetry [23, 151] and in 3 dimensions  show that n = 0 is a global attractor and the n = 1 solution is the critical solution (see also [67, 68] for computations of the largest perturbation-eigenvalues of W 0 and W 1). Again, for the wave map from 2+1 Minkowski to the 2-sphere generic singularity formation proceeds through adiabatic shrinking of a static solution .
These results have led to the suggestion in  that criticality (in the sense of the existence of a codimension-1 solution separating evolution towards qualitatively different end states) could be a generic and robust feature of evolutionary PDE systems in supercritical dimensions, and not an effect particular of gravity.
Garfinkle and Isenberg  examine the threshold between the round end state and pinching off in Ricci flow for a familiy of spherically symmetric geometries on S3. They have found intermediate approach to a special “javelin” geometry, but have not investigated whether this is universal. See also  and . Update
A scaling of the shape of the event horizon at the moment of merger in binary black hole mergers is noted in , but this is really a kinematic effect.
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