Constraining the Konoplya-Rezzolla-Zhidenko Deformation Parameters. II. Limits from Stellar-Mass Black Hole X-Ray Data

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 popular approach 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, and Zhidenko [Phys. Rev. D 93, 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.