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 that 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 α ₁₃ and α ₂₂, which quantify deviations from the Kerr metric. For α ₂₂ = 0, we obtain the black hole spin and . For α ₁₃ = 0, we obtain and . The Kerr solution is recovered for α ₁₃ = α 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.

X-ray reflection spectroscopy is a powerful tool for probing the strong gravity region of black holes and can be used for testing general relativity in the strong field regime. Simplifications of the available relativistic reflection models limit the capability of performing accurate measurements of the properties of black holes. In this paper, we present an extension of the model relxill_nk in which the accretion disk has a finite thickness rather than being infinitesimally thin. We employ the accretion disk geometry proposed by Taylor & Reynolds and we construct relativistic reflection models for different values of the mass accretion rate of the black hole. We apply the new model to high-quality Suzaku data of the X-ray binary GRS 1915+105 to explore the impact of the thickness of the disk on tests of the Kerr metric.

Einstein’s theory of General Relativity predicts that the spacetime metric around astrophysical black holes is described by the Kerr solution. In this work, we employ state-of-the-art relativistic reflection modeling to analyze a selected set of NuSTAR spectra of Galactic black holes to obtain the most robust and precise constraints on the Kerr black hole hypothesis possible today. Our constraints are much more stringent than those from other electromagnetic techniques and, with some sources, we find stronger constraints than those currently available from gravitational waves.

We present the study of a sample of seven “bare” active galactic nuclei observed with Suzaku. We interpret the spectrum of these sources with a relativistic reflection component and we employ our model relxill_nk to test the Kerr nature of their supermassive black holes. We constrain the Johannsen deformation parameters α ₁₃ and α ₂₂, in which the Kerr metric is recovered when α ₁₃ = α ₂₂ = 0. All our measurements are consistent with the hypothesis that the spacetime geometry around these supermassive objects is described by the Kerr solution. For some sources, we obtain quite strong constraints on α ₁₃ and α ₂₂ when compared to those found in our previous studies. We discuss the systematic uncertainties in our tests and the implications of our results.

We analyze simultaneous observations with NuSTAR and Swift of the black hole binary GX 339–4 in which we clearly detect both a strong thermal component and prominent relativistic reflection features. We employ nkbb and relxill_nk, which are the state of the art of, respectively, the thermal and reflection models to test the Kerr black hole hypothesis. We obtain unprecedented precise measurements of the Johannsen deformation parameter α ₁₃: α 13 = − 0.012 − 0.039 + 0.011 (lamppost coronal geometry) and α 13 = − 0.010 − 0.018 + 0.024 (broken power-law emissivity profile) at a 90% confidence level, where the Kerr metric corresponds to α ₁₃ = 0. We investigate the systematic uncertainties by fitting the data with different models.

The iron-line and continuum-fitting methods are currently the two leading techniques for measuring black-hole spins with electromagnetic radiation. They can be naturally extended for probing the spacetime geometry around black holes and testing general relativity in the strong field regime. In the past couple of years, there has been significant work to use the iron-line method to test the nature of black holes. Here we use the continuum-fitting method and we show its capability of constraining the spacetime geometry around black holes by analyzing 17 Rossi X-ray Timing Explorer data of the X-ray binary LMC X-1.