On the Superradiance of Spin-1 Waves in an Equatorial Wedge around a Kerr Hole

Recently Van Putten has suggested that superradiance of magnetosonic waves in a toroidal magnetosphere around a Kerr black hole may play a role in the central engine of gamma-ray bursts. In this context, he computed (in the WKB approximation) the superradiant amplification of scalar waves confined to a thin equatorial wedge around a Kerr hole and found that the superradiance is higher than for radiation incident over all angles. This paper presents calculations of both spin-0 (scalar) superradiance (integrating the radial equation rather than using the WKB method) and and spin-1 (electromagnetic/magnetosonic) superradiance, in Van Putten's wedge geometry. In contrast to the scalar case, spin-1 superradiance decreases in the wedge geometry, decreasing the likelihood of its astrophysical importance.