The electric and magnetic conductivity of a Kerr hole

Abstract

We interpret the electromagnetic properties of a Kerr hole in terms of equal electric and magnetic conductivity. This accounts for the boundary conditions satisfied by electromagnetic fields at the horizon. We calculate the rate at which the hole should be heated by Ohmic dissipation, and find that it agrees with the First Law of Black Hole Thermodynamics. The dissipation manifests itself in the black hole energy-extraction mechanism of Blandford & Znajek as an effective internal resistance of magnitude 30 ohm. This results in the Eddington luminosity being an upper limit to the rate at which energy can be removed from a rotating black hole in an active galactic nucleus.