  We describe the first axisymmetric numerical code based on the generalized
harmonic formulation of the Einstein equations which is regular at the axis. We
test the code by investigating gravitational collapse of distributions of
complex scalar field in a Kaluza-Klein spacetime. One of the key issues of the
harmonic formulation is the choice of the gauge source functions, and we
conclude that a damped wave gauge is remarkably robust in this case. Our
preliminary study indicates that evolution of regular initial data leads to
formation both of black holes with spherical and cylindrical horizon
topologies. Intriguingly, we find evidence that near threshold for black hole
formation the number of outcomes proliferates. Specifically, the collapsing
matter splits into individual pulses, two of which travel in the opposite
directions along the compact dimension and one which is ejected radially from
the axis. Depending on the initial conditions, a curvature singularity develops
inside the pulses.

General Relativity and Quantum Cosmology;Solar and Stellar Astrophysics;High Energy Physics - Theory;Analysis of PDEs;Numerical Analysis;Computational Physics