The Blandford-Znajek Process as a Centeral Engine for a Gamma Ray Burst

We investigate the possibility that gamma-ray bursts are powered by a central engine consisting of a black hole with an external magnetic field anchored in a surrounding disk or torus. The energy source is then the rotation of the black hole, and it is extracted electromagnetically via a Poynting flux, a mechanism first proposed by Blandford and Znajek (1997) for AGN. Accounting both for the maximum rotation energy of the hole and for the efficiency of electromagnetic extraction, we find that a maximum of 9% of the rest mass of the hole can be converted to a Poynting flow, i.e. the energy available to produce a gamma-ray burst is 1.6 X 10^{53}M/M_{sun}erg for a black hole of mass M. We show that the black holes formed in a variety of gamma-rayburst scenarios probably contain the required high angular momentum. To extract the energy from a black hole in the required time \lsim1000s a field of 10^{15}G near the black hole is needed. We give an example of a disk-plus-field structure that both delivers the required field and makes the Poynting flux from the hole dominate that ofthe disk. Thereby we demonstrate that the Poynting energy extracted need not be dominated by the disk, nor is limited to the binding energy of the disk. This means that the Blandford-Znajek mechanism remains a very good candidate for powering gamma-ray bursts.