Towards precision tests of general relativity with black hole X-ray reflection spectroscopy.

Astrophysical black hole systems are the ideal laboratories for testing Einstein's theory of gravity in the strong field regime. We have recently developed a framework which uses the reflection spectrum of black hole systems to perform precision tests of general relativity by testing the Kerr black hole hypothesis. In this paper, we analyze XMM-Newton and NuSTAR observations of the supermassive black hole in the Seyfert 1 galaxy MCG-06-30-15 with our disk reflection model. We consider the Johannsen metric with the deformation parameters $\alpha_{13}$ and $\alpha_{22}$, which quantify deviations from the Kerr metric. For $\alpha_{22} = 0$, we obtain the black hole spin $0.928 < a_* < 0.983$ and $-0.44 < \alpha_{13} < 0.15$. For $\alpha_{13} = 0$, we obtain $0.885 < a_* < 0.987$ and $-0.12 < \alpha_{22} < 1.05$. The Kerr solution is recovered for $\alpha_{13} = \alpha_{22} = 0$. Thus, our results include the Kerr solution within statistical uncertainties. Systematic uncertainties are difficult to account for, and we discuss some issues in this regard.