The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

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We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations of the reflection spectrum of a thin accretion disk are split into two parts: the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. The transfer function only depends on the background metric and takes into account all the relativistic effects (gravitational redshift, Doppler boosting, and light bending). Our code computes the transfer function for a spacetime described by the Johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. Transfer functions and single line shapes in the Kerr metric are compared with those calculated from existing codes to check that we reach the necessary accuracy. We also simulate some observations with NuSTAR and LAD/eXTP and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the Kerr metric.

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 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 black hole spacetime. We show that the numerical error introduced by using a ray-tracing code is not significant as 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.

Recently, we have extended the x-ray reflection model RELXILL to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter α 13 . Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.

In this paper, we investigate the effects of a dark matter (DM) spike on the neighborhood of Sgr A*, the black hole (BH) in the center of the Milky Way. Our main goal is to investigate whether current and future astronomical observations of Sgr A* could detect the presence of such a DM spike. At first, we construct the spacetime metric around a static and spherically symmetric BH with a DM spike, and later, this solution is generalized for a rotating BH using the Newman–Janis–Azreg-Aïnou algorithm. For the static BH metric, we use the data of the S2 star orbiting Sgr A* to determine and analyze the constraints on the two free parameters characterizing the density and innermost boundary of the DM halo surrounding the BH. Furthermore, by making use of the available observational data for the DM spike density ρ sp and the DM spike radius R sp in the Milky Way, we consider a geometrically thick accretion disk model around the Sgr A* BH and demonstrate that the effect of DM distribution on the shadow radius and the image of the BH is considerably weak for realistic DM densities, becoming significant only when the DM density is of the order ρ sp ∼ (10−19–10−20) g cm−3 near the BH. We further analyze the possibility of observing this effect with radio interferometry, simulating observations with an EHT-like array, and find that it is unlikely to be detectable in the near future.

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 α13 and α22, which quantify deviations from the Kerr metric. For α22 = 0, we obtain the black hole spin 0.928 < a * < 0.983 and −0.44 < α13 < 0.15. For α13 = 0, we obtain 0.885 < a * < 0.987 and −0.12 < α22 < 1.05. The Kerr solution is recovered for α13 = α22 = 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.

Relativistic reflection features are commonly observed in the Xray spectra of accreting black holes. In the presence of high quality data and with the correct astrophysical model, X-ray reflection spectroscopy can be quite a powerful tool to probe the strong gravity region, study the morphology of the accreting matter, measure black hole spins, and possibly test Einstein's theory of general relativity in the strong field regime. In the last decade, there has been significant progress in the development of the