Total and Jet Blandford-Znajek Power in the Presence of an Accretion Disk

Rotating black holes probably power ultrarelativistic jets in gamma-ray bursts, relativistic jets from some active galactic nuclei, and jets from some black hole X-ray binaries. Prior estimates of the power output of a black hole have assumed an infinitely thin disk and a magnetic field based upon a slowly rotating black hole and have not self-consistently determined the geometry or magnitude of the magnetic field for a realistic accretion disk. We provide useful formulae for the total and jet Blandford-Znajek (BZ) power and efficiency as determined self-consistently from general relativistic magnetohydrodynamic numerical models. Of all jet mechanisms, we suggest that only the BZ mechanism is able to produce an ultrarelativistic jet.