Tests Of General Relativity Research Articles

Putting the Squeeze on General Relativity

Analyzing the first image of a black hole in a nearby galaxy, researchers have provided quantitative tests of general relativity in the strongest gravitational fields yet.

An optical perspective on the theory of relativity - II: Gravitational deflection of light and Shapiro time delay

By regarding a gravitational field as a special optical medium, we define its refractive index using the general form of the solution to the Einstein equation in general relativity. A generalized version of Snell's law is given by comparing the space structure of a gravitational field with that of optical medium. The applicability of Snell's law is extended from Euclidean space to a spherical symmetrical gravitational field space. Drawing upon the generalized version of Snell's law, geometrical optics are used to arrive at formulas for the gravitational deflection of light and Shapiro time delay in a spherically symmetric gravitational field. These formulas are identical to those obtained by using geodesic equations in general relativity, thus proving that a gravitational field is a special optical medium.

Can we use next-generation gravitational wave detectors for terrestrial precision measurements of Shapiro delay?

Shapiro time delay is one of the fundamental tests of general relativity and post-Newtonian theories of gravity. Consequently, its measurements can be used to probe the parameter γ which is related to spacetime curvature produced by a unit mass in the post-Newtonian formalism of gravity. To date all measurements of time delay have been conducted on astronomical scales. It was asserted in 2010 that gravitational wave detectors on Earth could be used to measure Shapiro delay on a terrestrial scale via massive rotating systems. Building on that work, we consider how measurements of Shapiro delay can be made using next-generation gravitational wave detectors. We perform an analysis for measuring Shapiro delay with the next-generation gravitational wave detectors Cosmic Explorer and Einstein Telescope to determine how precisely the effect can be measured. Using a rotating mass unit design, we find that Cosmic Explorer and Einstein Telescope can measure the Shapiro delay signal with amplitude signal to noise ratios upwards of ∼28 and ∼43 in 1 year of integration time, respectively. By measuring Shapiro delay with this technique, next-generation interferometers will allow for terrestrial measurements of γ in the paramaterized post-Newtonian formalism of gravity with sub-percent precision.

Classical tests of general relativity I: looking to the past to understand the present

Einstein’s theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as arousing substantial interest in topics related to gravitation. However, to understand present and future discoveries, it is convenient to look to the past, to the classical tests of GR, namely, the deflection of light by the Sun, the perihelion precession of Mercury, and the gravitational redshift of light. The objective of this work is to offer a non-technical introduction to the classical tests of GR. In this first part of the work, some basic concepts of relativity are introduced and the principle of equivalence is analysed. The second part of the article examines the classical tests.

Classical tests of general relativity II: looking to the past to understand the present

The objective of this second part of the work is to present heuristic derivations of the three classical tests of general relativity. These derivations are based on the Einstein equivalence principle and use Newtonian physics as a theoretical framework. The results obtained are close to Einstein’s original predictions. Historical and anecdotal aspects of the subject are also discussed.

Verification of Einstein’s Formula for Gravitational Deflection of Light Using Observations of Galactic Microlensing

General relativity (GR) has a solid experimental base. However, the emergence of new experimental capabilities and independent observational information stimulates continuing tests of general relativity. The purpose of this work is to evaluate the potential of gravitational microlensing of distant sources on the stars of our Galaxy and to verify Einstein’s formula of gravitational refraction. This effect has been repeatedly tested in the Solar System in high-accuracy experiments with the propagation of radio waves, when the measurements are most effective for the distances from the signal trajectory to the Sun on the order of several solar radii. In the case of galactic microlensing, a quite different type of observational data and other characteristic distances are used that are determined in the high magnification events by the Einstein ring radii, which is typically of the order of 1 AU. Although the gravitational deflections of light by stars are very small and currently practically inaccessible by direct measurements, nonetheless, due to the large distances to the microlenses, the radiation flux from the source in strong microlensing events can increase several times. To verify Einstein’s formula, a more general dependence of the beam deflection angle $$\alpha \propto 1/{{p}^{{1 + \varepsilon }}}$$ on its impact distance p relative to the deflector is considered and, accordingly, the equations of gravitational lensing are modified. The challenge is to limit e based on observational data. The Early Warning System data obtained in 2018 within the Optical Gravitational Lensing Experiment (OGLE) ( http://ogle.astrouw.edu.pl/ogle4/ ews/2019/ews.html ) was used. A sample of 100 light curves from the data obtained by the OGLE group in 2018 was formed. Each light curve was fitted as part of a modified model of gravitational lensing with parameter e. As a result, 100 values of e and estimates of their variances were obtained. It was found that the mean value of e does not contradict GR within the limits of a one percent standard deviation. In the future, using a larger number of light curves will allow one to hope for a significant decrease in the error of e due to statistical averaging.

Slowly rotating topological neutron stars: universal relations and epicyclic frequencies

In the modern era of abundant X-ray detections and the increasing momentum of gravitational waves astronomy, tests of general relativity in strong field regime become increasingly feasible and their importance for probing gravity cannot be understated. To this end, we study the characteristics of slowly rotating topological neutron stars in the tensor-multi-scalar theories of gravity following the static study of this new type of compact objects by two of the authors. We explore the moment of inertia and verify that universal relations known from general relativity hold for this new class of compact objects. Furthermore, we study the properties of their innermost stable circular orbits and the epicyclic frequencies due to the latter’s hinted link to observational quantities such as quasi-periodic X-ray spectrum features.

Properties and Astrophysical Implications of the 150 M⊙ Binary Black Hole Merger GW190521

Abstract The gravitational-wave signal GW190521 is consistent with a binary black hole (BBH) merger source at redshift 0.8 with unusually high component masses, 85 − 14 + 21 M ⊙ and 66 − 18 + 17 M ⊙, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range 65–120 M ⊙. The probability that at least one of the black holes in GW190521 is in that range is 99.0%. The final mass of the merger ( 142 − 16 + 28 M ⊙) classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular BBH coalescence, we detail the physical properties of GW190521’s source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of the coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be 0.13 − 0.11 + 0.30 Gpc − 3 yr − 1 . We discuss the astrophysical implications of GW190521 for stellar collapse and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescences, or via hierarchical mergers of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary.

Verification of Einstein’s formula for gravitational deflection of light using observations of galactic microlensing

The potential of the gravitational microlensing inside our Galaxy for testing the Einstein formula for the gravitational light deflection is discussed. For this purpose, the lens mapping is modified by introducing parameter eps, which characterizes the deviation from this formula. An example of such deviation described by a simple power law is analyzed. We formed a sample of 100 microlensing light curves using the data of the Optical Gravitational Lensing Experiment (OGLE) for 2018. The resulting eps value does not contradict the General Relativity within 1 percent errors.

Gravitational-wave constraints on an effective-field-theory extension of general relativity

Gravitational-wave observations of coalescing binary systems allow for novel tests of the strong-field regime of gravity. Using data from the Gravitational Wave Open Science Center (GWOSC) of the LIGO and Virgo detectors, we place the first constraints on an effective field-theory based extension of General Relativity in which only higher-order curvature terms are added to the Einstein-Hilbert action. We construct gravitational-wave templates describing the quasi-circular, adiabatic inspiral phase of binary black holes in this extended theory of gravity. Then, after explaining how to properly take into account the region of validity of the effective field theory when performing tests of General Relativity, we perform Bayesian model selection using the two lowest-mass binary black-hole events reported to date by LIGO and Virgo -- GW151226 and GW170608 -- and constrain this theory with respect to General Relativity. We find that these data disfavors the appearance of new physics on distance scales around $\sim 150$ km. Finally, we describe a general strategy for improving constraints as more observations will become available with future detectors on the ground and in space.

Returning radiation in strong gravity around black holes: reverberation from the accretion disc

ABSTRACT We study reflected X-ray emission that returns to the accretion disc in the strong gravitational fields around black holes using General Relativistic ray-tracing and radiative transfer calculations. Reflected X-rays that are produced when the inner regions of the disc are illuminated by the corona are subject to strong gravitational light bending, causing up to 47 per cent of the reflected emission to be returned to the disc around a rapidly spinning black hole, depending upon the scale height of the corona. The iron Kα line is enhanced relative to the continuum by 25 per cent, and the Compton hump by up to a factor of 3. Additional light traveltime between primary and secondary reflections increases the reverberation time lag measured in the iron K band by 49 per cent, while the soft X-ray lag is increased by 25 per cent and the Compton hump response time is increased by 60 per cent. Measured samples of X-ray reverberation lags are shown to be consistent with X-rays returning to the accretion disc in strong gravity. Understanding the effects of returning radiation is important in interpreting reverberation observations to probe black holes. Reflected X-rays returning to the disc can be uniquely identified by blueshifted returning iron K line photons that are Compton scattered from the inner disc, producing excess, delayed emission in the 3.5–4.5 keV energy range that will be detectable with forthcoming X-ray observatories, representing a unique test of General Relativity in the strong field limit.

Dilaton-Axion Black Hole under the Solar System Tests

In the present paper we study the static and spherically symmetric dilaton-axion black hole in the testing ground of the Solar system. We constrain the parameters of the string motivated dilaton-axion form of the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In this case we have two free parameters: the dilaton strength and the point of curvature singularity of black hole. We obtain the permissible range of these two parameters from theoretical analysis based on the model and later compare them with the observations.

Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy and a Thin Disk Model with Finite Thickness

Abstract 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.

Testing gravity with cold-atom clocks in space

Atomic Clock Ensemble in Space (ACES) is a mission designed to test Einstein’s theory of General Relativity from the International Space Station (ISS). A primary frequency standard based on laser cooled caesium atoms (PHARAO) and an active H-maser (SHM) generate a clock signal that is distributed to a network of clocks on the ground to perform space-to-ground comparison. With a fractional frequency stability of 1 × 10−16 after 10 days of integration time and an accuracy of 1 – 2 × 10−16, ACES will provide an absolute measurement of the gravitational redshift, it will search for time variations of fundamental constant, and perform Standard Model Extension (SME) tests. The ACES payload is currently completing its qualification tests before flying. The mission status, the latest test results, and the ACES performance for testing General Relativity are discussed.

Testing General Relativity with the Stellar-mass Black Hole in LMC X-1 Using the Continuum-fitting Method

Abstract 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.

Black hole spectroscopy for KAGRA future prospect in O5

Ringdown gravitational waves of compact binary mergers are an important target to test general relativity. The main components of the ringdown waveform after merger are black hole quasinormal modes. In general relativity, all multipolar quasinormal modes of a black hole should give the same values of black hole parameters. Although the observed binary black hole events so far are not significant enough to perform the test with ringdown gravitational waves, it is expected that the test will be achieved in third generation detectors. The Japanese gravitational wave detector KAGRA, called bKAGRA for the current configuration, has started observation, and discussions for the future upgrade plans have also started. In this study, we consider which KAGRA upgrade plan is the best to detect the subdominant quasinormal modes of black holes in the aim of testing general relativity. We use a numerical relativity waveform as injected signals that contains two multipolar modes and analyze each mode by matched filtering. Our results suggest that the plan FDSQZ, which improves the sensitivity of KAGRA for broad frequency range, is the most suitable configuration for black hole spectroscopy.

Parameter estimation for tests of general relativity with the astrophysical stochastic gravitational wave background

Recent observations of gravitational waves from binary black holes and neutron stars allow us to probe the strong and dynamical field regime of gravity. On the other hand, a collective signal from many individual, unresolved sources results in what is known as a stochastic background. We here consider probing gravity with such a background from stellar-mass binary black hole mergers. We adopt a simple power-law spectrum and carry out a parameter estimation study with a network of current and future ground-based detectors by including both general relativistic and beyond general relativistic variables. For a network of second-generation detectors, we find that one can place meaningful bounds on the deviation parameter in the gravitational-wave amplitude if it enters at a sufficiently negative post-Newtonian order. However, such future bounds from a stochastic background are weaker than existing bounds from individual sources, such as GW150914 and GW151226. We also find that systematic errors due to mismodeling of the spectrum is much smaller than statistical errors, which justifies our use of the power-law model. Regarding a network of third-generation detectors, we find that the bounds on the deviation parameter from statistical errors improve upon the second-generation case, though systematic errors now dominate the error budget and thus one needs to use a more realistic spectrum model. We conclude that individual sources seem to be more powerful in probing general relativity than the astrophysical stochastic background.

Hybrid Very Long Baseline Interferometry Imaging and Modeling with themis

Abstract Generating images from very long baseline interferometric observations poses a difficult, and generally not unique, inversion problem. This problem is simplified by the introduction of constraints, some generic (e.g., positivity of the intensity) and others motivated by physical considerations (e.g., smoothness, instrument resolution). It is further complicated by the need to simultaneously address instrumental systematic uncertainties and sparse coverage in the u–v plane. We report a new Bayesian image reconstruction technique in the parameter estimation framework Themis that has been developed for the Event Horizon Telescope. This has two key features: first, the full Bayesian treatment of the image reconstruction makes it possible to generate a full posterior for the images, permitting a rigorous and quantitative investigation into the statistical significance of image features. Second, it is possible to seamlessly incorporate directly modeled features simultaneously with image reconstruction. We demonstrate this second capability by incorporating a narrow, slashed ring in reconstructions of simulated M87 data in an attempt to detect and characterize the photon ring. We show that it is possible to obtain high-fidelity photon ring sizes, enabling mass measurements with accuracies of 2%–5% that are essentially insensitive to astrophysical uncertainties, and creating opportunities for precision tests of general relativity.

Earth-based clocks test general relativity

Optical clocks held at slightly different heights provide a stringent test of general relativity comparable to space experiments and open new opportunities for clock-based geophysical sensing.

Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently-developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to $120 M_\odot$ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.