  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.
