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.

We present the public release version of relxill_nk, an X-ray reflection model for testing the Kerr hypothesis and general relativity. This model extends the relxill model that assumes the black hole (BH) spacetime is described by the Kerr metric. We also present relxilllp_nk, the first non-Kerr X-ray reflection model with a lamppost corona configuration, as well as all other models available in the full relxill_nk package. In all models the relevant relativistic effects are calculated through a general relativistic ray-tracing code that can be applied to any well-behaved, stationary, axisymmetric, and asymptotically flat BH spacetime. We show that the numerical error introduced by using a ray-tracing code is not significant compared with the observational error present in current X-ray reflection spectrum observations. In addition, we present the reflection spectrum for the Johannsen metric as calculated by relxill_nk.

Observations of the black hole shadow of supermassive black holes, such as Sagittarius A* at the center of our Milky Way galaxy, allow us to study the properties of black holes and the nature of strong-field gravity. According to the Kerr hypothesis, isolated, stationary, and axisymmetric astrophysical black holes are described by the Kerr metric. The Kerr hypothesis holds in general relativity and in some modified gravity theories, but there are others in which it is violated. In principle, black hole shadow observations can be used to determine if the Kerr metric is the correct description for black holes, and in turn, they could be used to place constraints on modified gravity theories that do not admit the Kerr solution. We here investigate whether black hole shadow observations can constrain deviations from general relativity, focusing on two well-motivated modified quadratic gravity theories: Einstein-dilaton-Gauss–Bonnet gravity and dynamical Chern–Simons gravity. We show that current constraints on Einstein-dilaton-Gauss–Bonnet gravity are stronger than any that could be placed with black hole shadow observations of supermassive black holes. We also show that the same holds for dynamical Chern–Simons gravity through a systematic bias and a likelihood analysis when considering slowly-rotating supermassive black holes. However, observations of more rapidly-rotating black holes, with dimensionless spins , could be used to better constrain dynamical Chern–Simons gravity.

The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT) project, which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable.

Recently, two of us have found a family of singularity-free rotating black hole solutions in Einstein’s conformal gravity. These spacetimes are characterized by three parameters: the black hole mass $M$, the black hole spin angular momentum $J$, and a parameter $L$ that is not specified by the theory but can be expected to be proportional to the black hole mass $M$. The Kerr black hole solution of Einstein’s gravity is recovered for $L=0$. In a previous paper, we showed that X-ray data of astrophysical black holes require $L/M<1.2$. In the present paper, we report the results of a more sophisticated analysis. We apply the X-ray reflection model relxill_nk to NuSTAR and Swift data of the supermassive black hole in 1H0707–495. We find the constraint $L/M<0.45$ (90% confidence level).

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.