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Accretion disks around black holes radiate a significant fraction of the restmass of the accreting material in the form of thermal radiation from within afew gravitational radii of the black hole ($ r \lesssim 20 G M / c^{2}$). Inaddition, the accreting matter may also be illuminated by hard X-rays from thesurrounding plasma which adds fluorescent transition lines to the emission.This radiation is emitted by matter moving along geodesics in the metric,therefore the strong Doppler and gravitational redshifts observed in theemission encode information about the strong gravitational field around theblack hole. In this paper the possibility of using the X-ray emission as astrong field test of General Relativity is explored by calculating the spectrafor both the transition line and thermal emission from a thin accretion disk ina series of parametrically deformed Kerr metrics. In addition the possibilityof constraining a number of known black hole spacetimes in alternative theoriesof gravity is considered.

Testing the "no-hair" property of black holes with X-ray observations of accretion disks