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 in 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 get stronger constraints than those currently available from gravitational waves.
We continue exploring the constraining capabilities of X-ray reflection spectroscopy to test the Kerr-nature of astrophysical black holes and we present the results of our analysis of two NuSTAR observations of Cygnus X-1 in the soft state. We find that the final measurement can strongly depend on the assumption of the intensity profile. We conclude that Cygnus X-1 is not suitable for tests of general relativity using X-ray reflection spectroscopy and we discuss the desired properties of a source to be a good candidate for our studies.
Astrophysical black holes are ideal laboratories for testing Einstein's theory of general relativity in the strong field regime. In this manuscript, we present an analysis of Suzaku and NuSTAR spectra of the black hole binary Cygnus X-1 using RELXILL_NK. Unlike our previous study on Cygnus X-1 with NuSTAR data, here we are able to constrain the Johannsen deformation parameter $α_{13}$. However, despite the high energy resolution near the iron line provided by Suzaku, our constraints on the Kerr metric from Cygnus X-1 are not very stringent in comparison with those that have been obtained from …
We analyze the broad-band X-ray spectrum (0.3-50 keV) of the luminous Seyfert 1 / quasar PG 1211+143 - the archetypal source for high-velocity X-ray outflows - using near-simultaneous XMM-Newton and NuSTAR observations. We compare pure relativistic reflection models with a model including the strong imprint of photoionized emission and absorption from a high-velocity wind (Pounds16a,16b), finding a spectral fit that extrapolates well over the higher photon energies covered by NuSTAR. Inclusion of the high S/N XMM-Newton spectrum provides much tighter constraints on the model parameters, with a…
Einstein's theory of General Relativity was proposed over 100 years ago and has successfully passed a large number of observational tests in weak gravitational fields. On the contrary, the strong field regime is still largely unexplored. Astrophysical black holes are ideal laboratories for testing gravity in the strong field regime. Here I will briefly review the current efforts of my group to test the strong gravitational field around black holes using X-ray data from NuSTAR, RXTE, Suzaku, and XMM-Newton.
The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$α$ lines are commonly observed in the X-ray spectrum of black holes and originate by X-ray fluorescence of the inner accretion disk. The profile of the iron line is sensitively affected by the spacetime geometry in the strong gravity region and can be used to test the Kerr black hole hypothesis. In this paper, we extend previous work in the literature. In particular: i) as…
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 review our current efforts to test General Relativity in the strong field regime by studying the reflection spectrum of supermassive black holes. So far we have analyzed 11 sources with observations of NuSTAR, Suzaku, Swift, and XMM-Newton. Our results are consistent with general relativity, according to which the spacetime metric around astrophysical black holes should be well approximated by the Kerr solution. We discuss the systematic uncertainties in our model and we present a preliminary study on the impact of some of them on the measurement of the spacetime metric.
Einstein's theory of General Relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and observations of binary pulsars. Thanks to a new generation of observational facilities, the past 5 years have seen remarkable changes in this field and there are now numerous efforts for testing General Relativity in the strong field regime with black holes and neutron stars using different techniques. Here I will review the work of my group at Fudan University devoted to test General Relativity with bl…
X-ray reflection spectroscopy is potentially a powerful tool to probe the spacetime geometry around astrophysical black holes and test general relativity in the strong field regime. However, precision tests of general relativity are only possible if we employ the correct astrophysical model and we can limit the systematic uncertainties. It is thus crucial to select the sources and the observations most suitable for these tests. In this work, we analyze simultaneous observations of XMM-Newton and NuSTAR of the supermassive black hole in Fairall 9. This source has a number of properties that mak…
We show how the model of pseudo-complex general relativity can be tested using gravitational wave signals from coalescing compact objects. The model, which agrees with Einstein gravity in the weak-field limit, diverges dramatically in the near-horizon regime, with certain parameter ranges excluding the existence of black holes. We show that simple limits can be placed on the model in both the inspiral and ringdown phase of coalescing compact objects. We discuss further how these bounds relate to current observational limits. In particular, for minimal scenarios previously considered in the lit…
The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. The past five years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and mm Very Long Baseline Interferometry observations. Here I summarize the state-of-the-art of the tests of General Relativity with black hole X-ray data, discussing its recent progress and future development…
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurat…
The iron line and the 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. In this Letter, we use the continuum-fitting method and we show its capability of constraining the spacetime geometry around black holes by analyzing 17 RXTE data of the X-ray bina…
The recent observation of high-energy astrophysical neutrinos can be used to constrain violations of Lorentz invariance emerging from a quantum theory of gravity. We perform threshold and Cherenkov analyses that improve existing bounds by factors ranging from about a million to 10^{20}.
Observations of gamma-ray bursts are being used to test for a momentum dependence of the speed of photons, partly motivated by preliminary results reported in analyses of some quantum-spacetime scenarios. The relationship between time of arrival, momentum of the photon and redshift of the source which is used for these purposes assumes a "breakdown" of relativistic symmetries, meaning that it is a preferred-frame scenario which does not satisfy the Relativity Principle. The alternative hypothesis of a "deformation" of relativistic symmetries, which preserves the Relativity Principle by adoptin…
X-ray reflection spectroscopy is a promising technique for testing general relativity in the strong field regime, as it can be used to test the Kerr black hole hypothesis. In this context, the parametrically deformed black hole metrics proposed by Konoplya, Rezzolla \& Zhidenko (Phys. Rev. D93, 064015, 2016) form an important class of non-Kerr black holes. We implement this class of black hole metrics in \textsc{relxill\_nk}, which is a framework we have developed for testing for non-Kerr black holes using X-ray reflection spectroscopy. We perform a qualitative analysis of the effect of the le…
In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that the well-known dependence of Bayes factors on the analysis priors in regions of the parameter space without likelihood support can lead to strong confidence in favor of incorrect conclusions when one employs the multiplicative Bayes factor. Bayes factors $\mathcal{O}(1)$ are ambivalent as they depend sensitively on the analysis priors, which are rarely set in…
The ULIRG Mrk 273 contains two infrared nuclei, N and SW, separated by 1 arcsec. A Chandra observation has identified the SW nucleus as an absorbed X-ray source with nH ~4e23 cm-2 but also hinted at the possible presence of a Compton thick AGN in the N nucleus, where a black hole of 10^9 Msun is inferred from the ionized gas kinematics. The intrinsic X-ray spectral slope recently measured by NuSTAR is unusually hard (photon index of ~1.3) for a Seyfert nucleus, for which we seek an alternative explanation. We hypothesise a strongly absorbed X-ray source in N, of which X-ray emission rises stee…
Einstein's gravity has been extensively tested in the weak field regime, primarily with experiments in the Solar System and observations of binary pulsars, and current data agree well with theoretical predictions. On the other hand, strong gravity is largely unexplored and there are a number of theories beyond Einstein's gravity that make the same predictions for weak fields and present deviations only when gravity becomes strong. The best laboratory for testing strong gravity is the spacetime around astrophysical black holes. X-ray reflection spectroscopy can be a powerful tool to probe the s…
General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part of this thesis, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in general relativity in terms of their masses and spins and which states that these compact objects are described by the Kerr metric. I invest…
We use the Relativistic Precession Model (RPM) (Stella et al. 1999a) and quasi-periodic oscillation (QPO) observations from the Rossi X-ray Timing Explorer to derive constraints on the properties of the black holes that power these sources and to test General Relativity (GR) in the strong field regime. We extend the techniques outlined by Motta et al. (2014a,b) to use pairs of simultaneously measured QPOs, rather than triplets, and extend the underlying spacetime metric to constrain potential deviations from the predictions of GR for astrophysical black holes. To do this, we modify the RPM mod…
In this paper, we briefly present RELXILL_NK, the first and currently only readily available model of the relativistic reflection spectrum of black hole accretion disks that includes non-Kerr solutions for the black hole spacetime, thus allowing for tests of the Kerr hypothesis and GR. RELXILL_NK makes use of a general relativistic ray-tracing code to calculate the relativistic effects of any well-behaved, stationary, axisymmetric, and asymptotically flat black hole spacetime, while the disk physics is handled through the non-relativistic X-ray reflection code XILLVER. A number of different fl…
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 $α_{13}$ and $α_{22}$, which quantify deviations from the…
Testing Source Dependence in Gravitational-Wave Tests of General Relativity with Mutual Information
Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）
Gravitational-wave observations of binary black holes allow new tests of general relativity to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal, otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with general relativity. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more strin…
The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can…
Blazars are a peculiar class of active galactic nuclei (AGNs) that enlighten the sky at all wavelengths. The electromagnetic emission of these sources is jet-dominated resulting in a spectral energy distribution (SED) that has a typical double-humped shape. X-ray photons provide a wealth of information on the physics of each source as in the X-ray band we can observe the tail of SED first peak, the rise of the second one or the transition between the two. NuSTAR, thanks to its capability of focusing X-rays up to 79 keV provides broadband data particularly suitable to compute SEDs in a still po…
X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we use a general relativistic magnetohydrodynamic (GRMHD) code to generate a thin accretion disk in Kerr spacetime and ray-tracing techniques to calculate its relativistically broadened reflection spectru…
It is known that massive black holes (MBHs) of $10^{5-7}\,M_\odot$ could capture small compact objects to form extreme-mass-ratio inspirals (EMRIs). Such systems emit gravitational waves (GWs) in the band of the Laser Interferometer Space Antenna (LISA) and are ideal probes of the space-time geometry of MBHs. Recently, we have shown that MBHs could also capture stellar-mass binary black holes (about $10\,M_\odot$) to form binary-EMRIs (b-EMRIs) and, interestingly, a large fraction of the binaries coalesce due to the tidal perturbation by the MBHs. Here we further show that the coalescence coul…
Today we have quite stringent constraints on possible violations of the Weak Equivalence Principle from the comparison of the acceleration of test-bodies of different composition in Earth's gravitational field. In the present paper, we propose a test of the Weak Equivalence Principle in the strong gravitational field of black holes. We construct a relativistic reflection model in which either the massive particles of the gas of the accretion disk or the photons emitted by the disk may not follow the geodesics of the spacetime. We employ our model to analyze the reflection features of a NuSTAR …
The continuum-fitting and the iron-line methods are currently the two leading techniques for measuring the spins of accreting black holes. In the past few years, these two methods have been developed for testing fundamental physics. In the present work, we employ state-of-the-art models to test black holes through the continuum-fitting and the iron-line methods and we analyze three NuSTAR observations of the black hole binary GRS 1716-249 during its outburst in 2016-2017. In these three observations, the source was in a hard-intermediate state and the spectra show both a strong thermal compone…
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% c…
Astrophysical black holes are thought to be the Kerr black holes predicted by general relativity, but macroscopic deviations from the Kerr solution can be expected from a number of scenarios involving new physics. In Paper I, we studied the reflection features in NuSTAR and XMM-Newton spectra of the supermassive black hole at the center of the galaxy MCG-06-30-15 and we constrained a set of deformation parameters proposed by Konoplya, Rezzolla & Zhidenko (Phys. Rev. D93, 064015, 2016). In the present work, we analyze the X-ray data of a stellar-mass black hole within the same theoretical frame…
Einstein-Maxwell dilaton-axion gravity is a string-inspired model arising from the low energy effective action of heterotic string theory and an important candidate as alternative to General Relativity. Recently, some authors have explored its astrophysical implications in the spectra of accreting black holes and inferred the constraint $r_2 < 0.1$, where $r_2 \ge 0$ is the black hole dilaton charge and General Relativity is recovered for $r_2 = 0$. In the present paper, we study the impact of a non-vanishing black hole dilaton charge on the reflection spectrum of the disk. From the analysis o…
We test the two-corona accretion scenario for active galactic nuclei in the case of the `bare' Seyfert 1 galaxy HE 1143-1810. We perform a detailed study of the broad-band UV--X-ray spectral properties and of the short-term variability. We present results of a joint XMM-Newton and NuSTAR monitoring of the source, consisting of 5x20 ks observations, each separated by 2 days, performed in December 2017. The source is variable in flux among the different observations, and a correlation is observed between the UV and X-ray emission. Moderate spectral variability is observed in the soft band. The t…
In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A* (Sgr A*) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of S…
Binary pulsars allow us to carry out precision tests of gravity and have placed stringent bounds on a broad class of theories beyond general relativity. Current and future radio telescopes, such as FAST, SKA, and MeerKAT, may find a new astrophysical system, a pulsar orbiting around a black hole, which will provide us a new source for probing gravity. In this paper, we systematically study the prospects of testing general relativity with such black hole-pulsar binaries. We begin by finding a mapping between generic non-Einsteinian parameters in the orbital decay rate and theoretical constants …
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 sop…
Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but the actual nature of these objects has still to be proven. The Kerr black hole hypothesis can be tested by observing strong gravity features and check if they are in agreement with the predictions of General Relativity. In particular, the study of the properties of the electromagnetic radiation emitted by the gas of the accretion disk can provide information on the geometry of the space-time around these objects and constrain possible deviations from the Kerr background.
Observations of compact objects in the electromagnetic spectrum and the detection of gravitational waves from them can lead to quantitative tests of the theory of general relativity in the strong-field regime following two very different approaches. In the first approach, the general relativistic field equations are modified at a fundamental level and the magnitudes of the potential deviations are constrained by comparison with observations. In the second approach, the exterior spacetimes of compact objects are parametrized in a phenomenological way, the various parameters are measured observa…
The spacetime geometry around astrophysical black holes is well approximated by the Kerr metric, but deviations from standard predictions are possible in a number of scenarios beyond Einstein's gravity and in the presence of exotic matter. In this paper, we present the constraints on possible deviations from the Kerr solution using X-ray reflection spectroscopy from the analysis of real data. We use the relativistic X-ray reflection code RELXILL modified to a generic stationary, axisymmetric and asymptotically flat black hole metric. We analyze 350 ks long XMM-Newton observations of the AGN in…
Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity…
The direct detection of gravitational waves with upcoming second-generation gravitational wave detectors such as Advanced LIGO and Virgo will allow us to probe the genuinely strong-field dynamics of general relativity (GR) for the first time. We present a data analysis pipeline called TIGER (Test Infrastructure for GEneral Relativity), which is designed to utilize detections of compact binary coalescences to test GR in this regime. TIGER is a model-independent test of GR itself, in that it is not necessary to compare with any specific alternative theory. It performs Bayesian inference on two h…
The Event Horizon Telescope is a global very-long baseline interferometer capable of probing potential deviations from the Kerr metric, which is believed to provide the unique description of astrophysical black holes. Here we report an updated constraint on the quadrupolar deviation of Sagittarius A* within the context of a radiatively inefficient accretion flow model in a quasi-Kerr background. We also simulate near-future constraints obtainable by the forthcoming eight-station array and show that in this model already a one-day observation can measure the spin magnitude to within $0.005$, th…
Recently the Fermi GBM and LAT Collaborations reported their new observational data disfavoring quite a number of the quantum gravity theories, including the one suggesting the nonlinear (logarithmic) modification of a quantum wave equation. We show that the latter is still far from being ruled out: it is not only able to explain the new data but also its phenomenological implications turn out to be more vast (and more interesting) than one expected before.
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 ligh…
The blazar OJ287 is the most promising (and the only) case for an extragalactic binary black hole system inspiralling under the action of gravitational radiation reaction. At present, though it is not possible to directly observe the binary components, it is possible to observe the jet emanating form the primary black hole. We argue that the orbital motion of the secondary black hole is reflected in the wobble of the jet and demonstrate that the wobble is orbital position dependent. The erratic wobble of the jet, reported in Agudo et al. (2012), is analyzed by taking into account the binary na…
