Charged Rotating Black Hole Formation from Thin Shell Collapse in Three Dimensions

The thin shell collapse leading to the formation of charged rotating black holes in 2+1 dimensions is analyzed in the light of a recently developed Hamiltonian formalism for these systems. It is proposed to demand, as a natural extension of what happens with a solenoid in flat space, that the magnetic field should vanish just outside the shell. The adoption of this boundary condition results in an exterior solution with a magnetic field different from zero at a finite distance from the shell. The interior solution is also found and assigns another interpretation, in a different context, to the magnetic solution previously obtained by Hirschmann and Welch.