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

A rotating black hole probably powers 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, 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.