Numerical studies of critical collapse should go beyond spherical symmetry (and in the first instance to axisymmetry) for three reasons:

- Weak gravitational waves in vacuum general relativity can focus and collapse. The black hole threshold in this process shows what in critical phenomena in gravitational collapse is intrinsic to gravity rather than the matter model.
- Black holes are characterised by charge and angular momentum as well as mass. Angular momentum is the more interesting of the two because it is again independent of matter, but cannot be studied in spherical symmetry.
- Angular momentum resists collapse, but angular momentum in the initial data is needed to
make a black hole with angular momentum. Therefore it is an interesting question to ask what
happens to the dimensionless ratio J/M
^{2}at the black hole threshold.

In the following we review what has been done so far.

5.1 Perturbative approach to angular momentum

5.2 Axisymmetric vacuum gravity

5.3 Scalar field

5.4 Neutron star collision in axisymmetry

5.5 Black hole collisions

5.2 Axisymmetric vacuum gravity

5.3 Scalar field

5.4 Neutron star collision in axisymmetry

5.5 Black hole collisions

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