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

TL;DR

This paper investigates the formation of charged rotating black holes in three dimensions through thin shell collapse, using a Hamiltonian formalism and novel boundary conditions to reconcile magnetic field properties.

Contribution

It introduces a new boundary condition for magnetic fields in thin shell collapse, leading to a consistent exterior magnetic solution in three-dimensional black hole formation.

Findings

Boundary condition results in non-zero magnetic field at finite distance

Interior solution offers a new interpretation of magnetic black holes

Method reconciles properties of solenoid and magnetic black holes

Abstract

The thin shell collapse leading to the formation of charged rotating black holes in three dimensions is analyzed in the light of a recently developed Hamiltonian formalism for these systems. It is proposed to demand, as a way to reconcile the properties of an infinitely extended solenoid in flat space with a magnetic black hole in three dimensions, 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 Cl\'{e}ment and by Hirschmann and Welch.