  Relativistic reflection features in the X-ray spectra of black hole binaries
and AGNs are thought to be produced through illumination of a cold accretion
disk by a hot corona. In this work, we assume that the corona has the shape of
an infinitesimally thin disk with its central axis the same as the rotational
axis of the black hole. The corona can either be static or corotate with the
accretion disk. We calculate the disk's emissivity profiles and iron line
shapes for a set of coronal radii and heights. We incorporate these emissivity
profiles into RELXILL_NK and we simulate some observations of a black hole
binary with NuSTAR to study the impact of a disk-like coronal geometry on the
measurement of the properties of the system and, in particular, on the
possibility of testing the Kerr nature of the source. We find that, in general,
the astrophysical properties of the accretion disk are recovered well even if
we fit the data with a model employing a broken power-law or a lamppost
emissivity profile, while it is more challenging to constrain the geometric
properties of the black hole spacetime.
