Classical axisymmetric gravity in real Ashtekar variables

We set up axisymmetric general relativity in terms of real
Ashtekar--Barbero variables. We analyze the constraints and equations of motion and show
how the Kerr, Schwarzschild and Minkowski solutions arise. We also
discuss boundary conditions. This opens the possibility of a
midisuperspace quantization using loop quantum gravity techniques for
spacetimes with axial symmetry and time dependence.