  X-ray reflection spectroscopy is a powerful technique for probing the nature
of gravity around black holes in the so-called strong field regime. One of the
most popular of such probes is to look at theory-agnostic deviations away from
the Kerr solution, which is the only astrophysically relevant black hole
solution within classical general relativity, in order to verify whether
astrophysical black holes are described by the Kerr metric. We have recently
extended our X-ray reflection spectroscopy framework to a class of very general
axisymmetric non-Kerr black holes proposed by Konoplya, Rezzolla & Zhidenko
(Phys. Rev. D93, 064015, 2016). Here, we analyze XMM-Newton and NuSTAR
observations of the supermassive black hole in the Seyfert 1 galaxy
MCG-06-30-15 with six different deviation parameters of this extended model. We
recover the Kerr solution in all cases, but some deformation parameters are
poorly constrained. We discuss the implications of this verification and future
possibilities.
