Testing General Relativity with black hole X-ray data: a progress report
Cosimo Bambi
备注：
8 pages, 3 figures. Talk given at the "International Workshop on Relativistic Astrophysics and Gravitation" (IWRAG-2021); Ulugh Beg Astronomical Institute, Uzbekistan, 12-14 May 2021
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 black hole X-ray data.
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.
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…
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.
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…
Creating a modified Belinfante/Rosenfeld procedure, Mathisson-Papapetrou-like equations are derived by which a comparison of General-Covariant Continuum Physics with General Relativity Theory becomes possible.
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.
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}.
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.
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…
We report on selected oral contributions to the A2 session "Mathematical relativity and other progress in classical gravity theory" of "The 20th International Conference on General Relativity and Gravitation (GR20)" in Warsaw.
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…
We present a Bayesian data analysis pipeline for testing GR using gravitational wave signals from coalescing compact binaries, and in particular binary neutron stars. In this study, we investigate its performance when sources with spins are taken into account.
Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.
Electron accelerations of the order of $10^{21} g$ obtained by laser fields open up the possibility of experimentally testing one of the cornerstones of general relativity, the weak equivalence principle, which states that the local effects of a gravitational field are indistinguishable from those sensed by a properly accelerated observer in flat space-time. We illustrate how this can be done by solving the Einstein equations in vacuum and integrating the geodesic equations of motion for a uniformly accelerated particle.
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 suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such as the standard Schwarzschild solution, or whether Nature prefers equivalent non-static solutions. This is a test of the boundary conditions of General Relativity rather than of the field equations. The fractional difference in clock rates between the two possibilities is a part in a hundred million. This is a large and easily measurable effect.
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…
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…
This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of General Relativity will be described. Then, the present situation will be reviewed presenting a number of examples. The opportunities given by astrophysical and astrometric observations will be shortly discussed. Coming to terrestrial experiments the attention will be specially focused on ringlasers and a dedicated experiment for the Gran Sasso Laboratories, n…
We discuss perspectives for new tests of general relativity which are based on recent technological developments as well as new ideas. We focus our attention on tests performed with atomic clocks and do not repeat arguments present in the other contributions to the present volume. In particular, we present the scientific motivations of the space projects ACES and SAGAS.
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…
In this paper the most recent developments in testing General Relativity in the gravitational field of the Earth with the technique of Satellite Laser Ranging are presented. In particular, we concentrate our attention on some gravitoelectric and gravitomagnetic post--Newtonian orbital effects on the motion of a test body in the external field of a central mass.
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…
Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we have applied the recently developed Extended General Relativistic theory to calculate the lower limit for the size of some relevant galaxies: the Milky Way, Andromeda and M87. Our results are in very good agreement with observations.
The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein's general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of te…
Recently, strong evidence was found for the presence of higher-order modes in the gravitational wave signals GW190412 and GW190814, which originated from compact binary coalescences with significantly asymmetric component masses. This has opened up the possibility of new tests of general relativity by looking at the way in which the higher-order modes are related to the basic signal. Here we further develop a test which assesses whether the amplitudes of sub-dominant harmonics are consistent with what is predicted by general relativity. To this end we incorporate a state-of-the-art waveform mo…
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found …
Deviations from general relativity, such as could be responsible for the cosmic acceleration, would influence the growth of large scale structure and the deflection of light by that structure. We clarify the relations between several different model independent approaches to deviations from general relativity appearing in the literature, devising a translation table. We examine current constraints on such deviations, using weak gravitational lensing data of the CFHTLS and COSMOS surveys, cosmic microwave background radiation data of WMAP5, and supernova distance data of Union2. Markov Chain Mo…
The inspirals of ``small'' ($1 - 100 M_\odot$) compact bodies through highly relativistic orbits of massive (several $\times 10^5 M_\odot -$ several $\times 10^6 M_\odot$) black holes are among the most anticipated sources for the LISA gravitational-wave antenna. The measurement of these waves is expected to map the spacetime of the larger body with high precision, allowing us to test in detail the hypothesis that black hole candidates are described by the Kerr metric of general relativity. In this article, we will briefly describe how these sources can be used to perform such a test. These pr…
The multiple detections of gravitational waves by LIGO (the Laser Interferometer Gravitational-Wave Observatory), operated by Caltech and MIT, have been acclaimed as confirming Einstein's prediction, a century ago, that gravitational waves propagating as ripples in spacetime would be detected. Yunes and Pretorius (2009) investigate whether LIGO's template-based searches encode fundamental assumptions, especially the assumption that the background theory of general relativity is an accurate description of the phenomena detected in the search. They construct the parametrized post-Einsteinian (pp…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes involving spacecraft navigation, geodesy and time transfer. Here I review the foundations of general relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for the new generation of high-accuracy tests of new physics beyond general relativity. Space-based experiments in fundamental physics are capable today to uniquely …
Laser ranging satellites have proved their efficiency for high precision testing of the effect of frame-dragging, one of remarkable predictions of the General Relativity. The analysis of the randomness properties of the residuals of LAGEOS and LAGEOS 2 satellites reveals the role of the thermal thrust -- Yarkovsky effect -- on the satellite which was in the orbit for longer period (LAGEOS). We also compute Earth's tidal modes affecting the satellite LARES. The recently obtained 5\% accuracy limit reached for the frame dragging effect based on the 3.5 year data of LARES analysed together with t…
The paper discusses the optimal conguration of one or more ring lasers to be used for measuring the general relativistic effects of the rotation of the earth, as manifested on the surface of the planet. The analysis is focused on devices having their normal vector lying in the meridian plane. The crucial role of the evaluation of the angles is evidenced. Special attention is paid to the orientation at the maximum signal, minimizing the sensitivity to the orientation uncertainty. The use of rings at different latitudes is mentioned and the problem of the non-sfericity of the earth is commented.
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 …
We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock experiments support local position invariance. Together these results confirm the Einstein Equivalence Principle which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relati…
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…
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.
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…
In this paper I investigate the possibility to test Einstein's equations with observations of cosmological large scale structure. I first show that we have not tested the equations in observations concerning only the homogeneous and isotropic Universe. I then show with several examples how we can do better when considering the fluctuations of both, the energy momentum tensor and the metric. This is illustrated with galaxy number counts, intensity mapping and cosmic shear, three examples that are by no means exhaustive.
We have reconstructed possible orbits for a collection of stars located within 0.5 arcsec of Sgr A*. These orbits are constrained by observed stellar positions and angular proper motions. The construction of such orbits serves as a baseline from which to search for possible deviations due to the unseen mass distribution in the central 1000 AU of the Galaxy. We also discuss the likelihood that some of these stars may eventually exhibit detectable relativistic effects, allowing for interesting tests of general relativity around the 2.6 x 10^6 solar mass central object.
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible …
Einstein theory can be embedded in Kaluza-Klein theory, and in particular all 4D vacuum solutions can be embedded in 5D (pure) canonical space where spacetime is independent of the extra coordinate. The uniqueness of 5D canonical space is quickly reproven, and its history and implications briefly reviewed. For 4D anti-deSitter space, the 5D space involves a wave running around spacetime, with an associated particle that has a local value of the cosmological 'constant' proportional to the square of the mass.
