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 .