  Accretion disks around black holes radiate a significant fraction of the rest
mass of the accreting material in the form of thermal radiation from within a
few gravitational radii of the black hole ($ r \lesssim 20 G M / c^{2}$). In
addition, the accreting matter may also be illuminated by hard X-rays from the
surrounding 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 the
emission encode information about the strong gravitational field around the
black hole. In this paper the possibility of using the X-ray emission as a
strong field test of General Relativity is explored by calculating the spectra
for both the transition line and thermal emission from a thin accretion disk in
a series of parametrically deformed Kerr metrics. In addition the possibility
of constraining a number of known black hole spacetimes in alternative theories
of gravity is considered.
