  The Blandford-Znajek mechanism is the continuous extraction of energy from a
rotating black hole via plasma currents flowing on magnetic field lines
threading the horizon. In the discovery paper, Blandford and Znajek
demonstrated the mechanism by solving the equations of force-free
electrodynamics in a perturbative expansion valid at small black hole spin.
Attempts to extend this perturbation analysis to higher order have encountered
inconsistencies.We overcome this problem using the method of matched asymptotic
expansions, taking care to resolve all of the singular surfaces (light
surfaces) in the problem. Working with the monopole field configuration, we
show explicitly how the inconsistencies are resolved in this framework and
calculate the field configuration to one order higher than previously known.
However, there is no correction to the energy extraction rate at this order.
These results confirm the basic consistency of the split monopole at small spin
and lay a foundation for further perturbative studies of the Blandford-Znajek
mechanism.
