The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole

The spectrum of X-rays produced by an accretion disk around a black hole is influenced markedly by Doppler shifls, gravitational red shifts, and the gravitational lens effect. These influences can be described by a "transfer function," which one folds into any assumed spectrum emitted on the disk's surface to get the spectrum observed at various locations far from the disk. This paper formulates such a transfer function and tabulates it for Kerr black holes of aIM = 0 and 0.9981. The transfer function depends strongly on the polar angle of the observer: An observer near the plane of the disk sees radiation from its hot inner regions to be less redshifted and to subtend a greater solid angle than does an observer near the disk's polar axis. Consequently, the equatorial observer sees a much harder spectrum at high energies than does the polar observer. This effect is more pronounced for black holes of larger angular momentum. Subject headings: black holes - gravitation - relativity - X-ray sources