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The spacetime geometry around astrophysical black holes is well approximatedby the Kerr metric, but deviations from standard predictions are possible in anumber of scenarios beyond Einstein's gravity and in the presence of exoticmatter. In this paper, we present the constraints on possible deviations fromthe Kerr solution using X-ray reflection spectroscopy from the analysis of realdata. We use the relativistic X-ray reflection code RELXILL modified to ageneric stationary, axisymmetric and asymptotically flat black hole metric. Weanalyze 350 ks long XMM-Newton observations of the AGN in MCG-06-30-15 takenduring July-August 2001 and constrain the Johannsen deformation parameter$\alpha_{13}$.

Testing general relativity with X-ray reflection spectroscopy of MCG-06-30-15