Tests Of General Relativity Research Articles

Explanation of Light Deflection, Precession of Mercury’s Perihelion, Gravitational Red Shift and Rotation Curves in Galaxies, by using General Relativity or equivalent Generalized Scalar Gravitational Potential, according to Special Relativity and Newtonian Physics

The development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR) is the mainstream approach of gravitational field. Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξ I) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξ I→ 0 and Special Relativity (SR) for ξ I=1. Moreover, the weak Equivalence Principle (EP) in the context of GSR, has the interpretation: m G=m, where m G and m are the gravitational mass and the inertial rest mass, respectively. In this paper, we bridge GR with GSR. This is achieved, by using a GSR-Lagrangian, which contains the corresponding GR-proper time. Thus, we obtain a new central scalar GSR-gravitational generalized potential V=V(k,l,r,r_dot,ϕ _dot), where k=k(ξ I), l=l(ξ I), r is the distance from the center of gravity and r_dot, ϕ _dot are the radial and angular velocity, respectively. The replacement k=1 and l=ξ I 2 makes the above GSR-potential equivalent to the original Schwarzschild Metric (SM). Thus, it explains the Precession of Mercury’s Perihelion (PMP), Gravitational Deflection of Light (GDL), Gravitational Red Shift (GRS) etc, by using SR and/or NPs. The procedure described in this paper can be applied to any other GR-spacetime metric, in order to find out the corresponding GSR-gravitational potential. So, we also use the GR-proper time of the 3rd Generalized Schwarzschild Metric (3GSM) and we obtain the central scalar GSR-gravitational potential V=V(a,k,l,r_dot,ϕ _dot), where a=a(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides the functions corresponding a=a(r). Thus, we obtain a new GSR-Gravitational field, which explains the PMP, GDL, GRS as well as the Rotation Curves in Galaxies, eliminating the corresponding DM.

Variant Mass for a Particle which Emits Gravitational Energy for a Particle Orbiting a Large Planet or Sun and for a Binary Star and Variant Frequency for the Light Passing Close a Gravitational Field from a Massive Object (Sun): The Physics and Emission of the Gravitational Energy

The Fundament of the Mass and the new theory and formula of the Variant Mass for a particle in Gravitation is presented at this research. Albert Einstein wrote in a research article: “Does the inertia of a body depend on its energy content?” (Ist die Trägheit eines Körpers von seimen Energienhalt abhängig?): “If a body emits energy E in the form of radiation, its mass decreases by E/ c2. The fact that the energy that leaves from the body is converted into radiation energy makes no difference, so the more general conclusion is reached that the mass of a body is a measure of the content of its energy ... It is not impossible that with bodies whose content of energy is highly variable (for example radio salts) the theory can be successfully tested. If the theory corresponds to the fact, radiation conducts inertia between the bodies that emit and absorb it”. Thus, Maxwell’s theory shows that electromagnetic waves are radiated (Maxwell Radiation) whenever charges accelerate as for example for the electron. Then, this electromagnetic radiation (photons) produces decreases in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by me at this research: Variant Mass for an Accelerated Charged Particle. For other hand, at the atom, the electron only radiates this energy when it jumps from one orbit to another orbit at the atom. It is in accordance with the experimental results from the spectral lines of the atom. The difference is that in a gravitational field the particle or a planet around the sun can take any position at the space and any radius. But, the electron at the atom only can take restricted positions which are explained by quantum mechanics, and the electrons don ́t emit radiation when they orbit around the nucleus. The discovery formula for the variant mass of the electron at the atom which describe exactly the variant mass of a charged particle at the atom which emits electromagnetic energy from one stationary level to other was demonstrated by myself a the research: The Fundament of the Mass: The Variant Mass for the electron at the atom. Besides, this is true for any type of radiation emitted: electromagnetic or gravitational energy which produce a decrease in the mass of the body. Therefore, the objective of this research is to demonstrate by theory, experiment and result the discovered formula which describe exactly the variant mass for a particle which emits gravitational energy. An example of the effect of this Gravitational energy emission is the light deflection for the light passing close the Sun (gravitational redshift frequency) and the Perihelion Precession of Mercury. Thus, the results of the mass formula are of great relevance for Gravitational Interactions. The results are in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star. It is in agreement with the experiment result and with the Theory of General Relativity. It is also demonstrated and explained the effects of the gravitation in a particle or light and the Perihelion Precession of Mercury. The formula for the gravitation redshift frequency, the wavelength, the light velocity, time measurement and the decreasing radius for a particle in a gravitational field are demonstrated. The formula of the light velocity is tested for the deflection of light passing close to the sun. The formula for time dilation and decrease distance are used to calculate the Perihelion Precession of Mercury. It is in agreement with the experiment result and with the Theory of General Relativity. The consequences of this research are amazing and in accordance with the same General Theory of Relativity, Newton Theory and with profound Insignia in Quantum Mechanics and for the Unification Theory

Cosmic Rays and Ultra High Energy Cosmic Rays (UHECR), GZK (Greisen-Zatsepin-Kuzmin) cutoff, Deflection angle of high energy cosmic rays in the propagation through the galactic and extragalactic magnetic fields, Auger Surface Detector and the Monitoring Data, Measurement of the Lifetime of Muons and Pions and The Variant Mass for a Particle in a Gravitational Field and the Binary Stars: The

The Surface Detector of the Pierre Auger Observatory consists of 1600 water Cherenkov tanks sampling ground particles of air showers produced by energetic cosmic rays. Every water tank is equipped with three photomultipliers (PMTs). Every 7 minutes monitoring data are recorded from each surface detector to ensure that they are performing as intended and also to understand the detector behavior. The monitoring data set is used to study the evolution of parameters of the PMTs as a function of both time and temperature. The main objective of the monitoring data is to monitor the stability of the PMTs. In case there is abnormal behavior detected, an alarm entry is created in the database. The classification of the alarms into different categories, corresponding to the observed patterns of the PMT variables and the decision of the alarm level are subject of this work. It is also researched the photomultipliers parameters and the alarm creation with examples of it: the Free Disk and High PMT gain change Alarms using c++, root and mysql. For other hand, it is researched about the measurement of the lifetime of muons and pions theoretically, experimentally and with the application of Statistics for the uncertainties of the results. The results have high accuracy and in accordance with the values of the literature. In addition, it is to analyze theoretically the deflection angle of the high energy cosmic rays in the propagation through the galactic and extragalactic magnetic fields. It is used the magnetic force formula and the Larmor radius, trigonometry, and the tables for the values of the galactic and extragalactic magnetic field and the distances to the galactic and extragalactic sources. It is possible to observe from this analysis that the deflection angles are very small for the considered cases. Thus, UHECR arrival directions should point back to their sources in the sky. Besides, it is researched about the GZK (Greisen-Zatsepin-Kuzmin) cutoff. A sharp cutoff at approximately several times 1019 eV in the energy spectrum of the cosmic rays is expected due to the energy degradation of the cosmic rays through their interaction with photons of the microwave background radiation. It is known as the GZK (Greisen-Zatsepin-Kuzmin) cutoff. A nucleon with an initial energy above Eo=1020 eV lose about 1/5 of Eo (initial energy) in each interaction. Thus, a nucleon of initial energy above 1020 eV will reduce its energy to 6*1019 eV (GZK cutoff energy) after traveling a distance of approximately 50 Mpc. For other hand, Albert Einstein wrote in a research article: “Does the inertia of a body depend on its energy content?” (Ist die Tragheit eines Korpers von seimen Energienhalt abhangig?): “If a body emits energy E in the form of radiation, its mass decreases by E/c2”. Thus, Maxwell's theory shows that electromagnetic waves are radiated whenever charges accelerate as for example for the electron. Then, this electromagnetic radiation (photons) produces a decrease in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by me at this research [34] and at the research of the Variant Mass of the Electron at the Atom. This is true for any type of radiation emitted: electromagnetic or gravitational energy which produce a decrease in the mass of the body. Therefore, other objective of this article is to demonstrate the discovered formula which describes exactly the variant mass for a particle which emits gravitational energy. An example of the effect of this Gravitational energy emission is the light deflection for the light passing close the Sun (gravitational redshift frequency) and the Perihelion Precession of Mercury. Thus, the results of the mass formula are of great relevance for Gravitational Interactions. The results are in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star. It is in agreement with the experiment result and with the Theory of General Relativity.

The BepiColombo solar conjunction experiments revisited

BepiColombo ESA/JAXA mission is currently in its 7 year cruise phase towards Mercury. The Mercury orbiter radioscience experiment (MORE), one of the 16 experiments of the mission, will start its scientific investigation during the superior solar conjunction (SSC) in March 2021 with a test of general relativity (GR). Other solar conjunctions will follow during the cruise phase, providing several opportunities to improve the results of the first experiment. MORE radio tracking system allows to establish precise ranging and Doppler measurements almost at all solar elongation angles (up to 7–8 solar radii), thus providing an accurate measurement of the relativistic time delay and frequency shift experienced by a radio signal during an SSC. The final objective of the experiment is to place new limits to the accuracy of the GR as a theory of gravity in the weak-field limit. As in all gravity experiments, non-gravitational accelerations acting on the spacecraft are a major concern. Because of the proximity to the Sun, the spacecraft will undergo severe solar radiation pressure acceleration, and the effect of the random fluctuations of the solar irradiance may become a significant source of spacecraft buffeting. In this paper we address the problem of a realistic estimate of the outcome of the SSC experiments of BepiColombo, by including in the dynamical model the effects of random variations in the solar irradiance. We propose a numerical method to mitigate the impact of the variable solar radiation pressure on the outcome of the experiment. Our simulations show that, with different assumptions on the solar activity and observation coverage, the accuracy attainable in the estimation of γ lays in the range [–] ×10−6.

Testing general relativity with x-ray reflection spectroscopy: The Konoplya-Rezzolla-Zhidenko parametrization

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 leading order strong-field deformation parameters on typical observables like the innermost stable circular orbits and the reflection spectra. We also present the first X-ray constraints on some of the deformation parameters of this metric, using \textit{Suzaku} data from the supermassive black hole in Ark~564, and compare them with those obtained (or expected) from other observational techniques like gravitational waves and black hole imaging.

Lensed gravitational waves: Scattering and applications

<p indent="0mm">The direct detection of gravitational waves from stellar-mass compact binary merger by ground-based laser interferometer gravitational wave detector LIGO/Virgo has verified the prediction of general relativity and opened a new chapter in gravitational wave astronomy. Up to now, a total of 50 gravitational wave events have been detected and published in GWTC-1 and GWTC-2 catalogue. In the near future, the third-generation ground based gravitational wave detector, such as the Einstein Telescope (ET), will be constructed with sensitivity improved by at least a factor of 10. Tens of thousands of gravitational wave signals are expected to be detected per year in the third-generation detector era. These gravitational wave signals will inevitably overlap with foreground massive celestial bodies (such as black hole, galaxy and galaxy cluster), thus leading to lensed gravitational wave signals which will undoubtedly be another important test of general relativity once detected. Furthermore, strongly lensed gravitational wave signals by galaxy from massive binary black hole could possibly be detected by future space detector, e.g., LISA and DECIGO. Since the wavelengths of gravitational waves are comparable with the size of some lens, the lensed gravitational waves play a unique role in studying the phenomena of wave nature, e.g., interference and diffraction. Lensed gravitational wave-electromagnetic wave system will have a wide range of applications in fundamental physics, cosmology and astrophysics when a series of lensed gravitational wave events and their corresponding electromagnetic counterparts have been detected. The most obvious advantage of lensed gravitational wave-electromagnetic wave system lies in that gravitational wave could provide time delay information with high accuracy, and electromagnetic wave could provide Fermat potential difference with high precision because a relatively complete arc of light could be obtained by electromagnetic wave observations and this is the most important step in measuring the Fermat potential. Thus, by combining the information from both approaches, lensed gravitational wave-electromagnetic wave system could be applied to study the speed of gravitational waves, constrain cosmological parameters, explore the substructure of the dark matter halo and investigate the lens model and so on. In this paper, we will review in detail how to use geodesic equation, lens equation, as well as wave equation to tackle the stationary scattering problem of lensed gravitational waves, and introduce how lensed gravitational wave-electromagnetic wave system could be applied to study the tensor properties, interference and diffraction effects of gravitational wave, as well as its applications in gravitational wave velocity, Hubble constant, cosmic curvature, lens mass, substructure and so on.

The shape of the black hole photon ring: A precise test of strong-field general relativity

We propose a new test of strong-field general relativity (GR) based on the universal interferometric signature of the black hole photon ring. The photon ring is a narrow ring-shaped feature, predicted by GR but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. We show that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of GR. We forecast that a tailored space-based interferometry experiment targeting M87* could test the Kerr nature of the source to the sub-sub-percent level.

Spin-Induced Black Hole Spontaneous Scalarization

We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins (a/M≳0.5). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations.

Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing

ABSTRACT We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$ by estimating the statistic EG, a probe of gravity, on cosmological scales $19 - 190\, h^{-1}{\rm Mpc}$. This is the highest redshift and largest scale estimation of EG so far. We use the quasar sample with redshifts 0.8 &amp;lt; z &amp;lt; 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_\ell ^{qq}$ and the redshift-space distortion parameter β are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_\ell ^{\kappa q}$ signal at $12\, \sigma$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at five bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at $1\, \sigma$ level over all these scales. With the CM estimated with 300 simulations, we report a best-fitting scale-averaged estimate of $E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm GR}(\bar{z})=0.33$ with Planck 2018 CMB + BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.

Gravitational wave peak luminosity model for precessing binary black holes

When two black holes merge, a tremendous amount of energy is released in the form of gravitational radiation in a short span of time, making such events among the most luminous phenomenon in the universe. Models that predict the peak luminosity of black hole mergers are of interest to the gravitational wave community, with potential applications in tests of general relativity. We present a surrogate model for the peak luminosity that is directly trained on numerical relativity simulations of precessing binary black holes. Using Gaussian process regression, we interpolate the peak luminosity in the 7-dimensional parameter space of precessing binaries with mass ratios $q\leq4$, and spin magnitudes $\chi_1,\chi_2\leq0.8$. We demonstrate that our errors in estimating the peak luminosity are lower than those of existing fitting formulae by about an order of magnitude. In addition, we construct a model for the peak luminosity of aligned-spin binaries with mass ratios $q\leq8$, and spin magnitudes $|\chi_{1z}|,|\chi_{2z}|\leq0.8$. We apply our precessing model to infer the peak luminosity of the GW event GW190521, and find the results to be consistent with previous predictions.

Atom-interferometric test of the universality of gravitational redshift and free fall

Light-pulse atom interferometers constitute powerful quantum sensors for inertial forces. They are based on delocalised spatial superpositions and the combination with internal transitions directly links them to atomic clocks. Since classical tests of the gravitational redshift are based on a comparison of two clocks localised at different positions under gravity, it is promising to explore whether the aforementioned interferometers constitute a competitive alternative for tests of general relativity. Here we present a specific geometry which together with state transitions leads to a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity. The proposed interferometer does not rely on a superposition of internal states, but merely on transitions between them, and therefore generalises the concept of physical atomic clocks and quantum-clock interferometry. An experimental realisation seems feasible with already demonstrated techniques in state-of-the-art facilities.

Modified Newtonian Gravity, Wide Binaries and the Tully-Fisher Relation

A recent study of a sample of wide binary star systems from the Hipparcos and Gaia catalogues has found clear evidence of a gravitational anomaly of the same kind as that appearing in galaxies and galactic clusters. Instead of a relative orbital velocity decaying as the square root of the separation, ΔV∝r−1/2, it was shown that an asymptotic constant velocity is reached for distances of order 0.1 pc. If confirmed, it would be difficult to accommodate this breakdown of Kepler’s laws within the current dark matter (DM) paradigm because DM does not aggregate in small scales, so there would be very little DM in a 0.1 pc sphere. In this paper, we propose a simple non-Newtonian model of gravity that could explain both the wide binaries anomaly and the anomalous rotation curves of galaxies as codified by the Tully-Fisher relation. The required extra potential can be understood as a Klein-Gordon field with a position-dependent mass parameter. The extra forces behave as 1/r on parsec scales and r on Solar system scales. We show that retrograde anomalous perihelion precessions are predicted for the planets. This could be tested by precision ephemerides in the near future.

Multiparameter Tests of General Relativity Using Multiband Gravitational-Wave Observations.

In this Letter, we show that multiband observations of stellar-mass binary black holes by the next generation of ground-based observatories (3G) and the space-based Laser Interferometer Space Antenna (LISA) would facilitate a comprehensive test of general relativity by simultaneously measuring all the post-Newtonian coefficients. Multiband observations would measure most of the known post-Newtonian phasing coefficients to an accuracy below a few percent-2 orders-of-magnitude better than the best bounds achievable from even "golden" binaries in the 3G or LISA bands. Such multiparameter bounds would play a pivotal role in constraining the parameter space of modified theories of gravity beyond general relativity.

Probing massive scalar and vector fields with binary pulsars

Precision tests of general relativity can be conducted by observing binary pulsars. Theories with massive fields exist to explain a variety of phenomena from dark energy to the strong CP problem. Existing pulsar binaries, such as the white dwarf-pulsar binary J1738+0333, have been used to place stringent bounds on the scalar dipole emission, and radio telescopes may detect a pulsar orbiting a black hole in the future. In this paper, we study the ability of pulsar binaries to probe theories involving massive scalar and vector fields through the measurement of the orbital decay rate. With a generic framework, we describe corrections to orbital decay rate due to (a) modification of GR quadrupolar radiation and (b) dipolar radiation of a massive field. We then consider three concrete examples: (i) massive Brans-Dicke theory, (ii) general relativity with axions, and (iii) general relativity with bound dark matter and a dark force. Finally, we apply direct observations of J1738 and simulations of a black hole-pulsar binary to bound theory parameters such as field's mass and coupling constant. We find new constraints on bound dark matter interactions with PSR J1738, and a black hole-pulsar discovery would likely improve these further. Such bounds are complementary to future gravitational-wave bounds. Regarding other theories, we find similar constraints to previous pulsar measurements for massive Brans-Dicke theory and axions. These results show that new pulsar binaries will continue to allow for more stringent tests of gravity.

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Understanding and improving the timing of PSR J0737−3039B

The double pulsar (PSR J0737−3039A/B) provides some of the most stringent tests of general relativity (GR) and its alternatives. The success of this system in tests of GR is largely due to the high-precision, long-term timing of its recycled-pulsar member, pulsar A. On the other hand, pulsar B is a young pulsar that exhibits significant short-term and long-term timing variations due to the electromagnetic-wind interaction with its companion and geodetic precession. Improving pulsar B’s timing precision is a key step towards improving the precision in a number of GR tests with PSR J0737−3039A/B. In this paper, red noise signatures in the timing of pulsar B are investigated using roughly a four-year time span, from 2004 to 2008, beyond which time the pulsar’s radio beam precessed out of view. In particular, we discuss the profile variations seen on timescales ranging from minutes – during the so-called “bright” orbital phases – to hours – during its full 2.5 h orbit – to years, as geodetic precession displaces the pulsar’s beam with respect to our line of sight. Also, we present our efforts to model the orbit-wide, harmonic modulation that has been previously seen in the timing residuals of pulsar B, using simple geometry and the impact of a radial electromagnetic wind originating from pulsar A. Our model successfully accounts for the long-term precessional changes in the amplitude of the timing residuals but does not attempt to describe the fast profile changes observed during each of the bright phases, nor is it able to reproduce the lack of observable emission between phases. Using a nested sampling analysis, our simple analytical model allowed us to extract information about the general properties of pulsar B’s emission beam, such as its approximate shape and intensity, as well as the magnitude of the deflection of that beam, caused by pulsar A’s wind. We also determined for the first time that the most likely sense of rotation of pulsar B, consistent with our model, is prograde with respect to its orbital motion. Finally, we discuss the potential of combining our model with future timing of pulsar B, when it becomes visible again, towards improving the precision of tests of GR with the double pulsar. The timing of pulsar B presented in this paper depends on the size of the pulsar’s orbit, which was calculated from GR, in order to precisely account for orbital timing delays. Consequently, our timing cannot directly be used to test theories of gravity. However, our modelling of the beam shape and radial wind of pulsar B can indirectly aid future efforts to time this pulsar by constraining part of the additional red noise observed on top of the orbital delays. As such, we conclude that, in the idealised case of zero covariance between our model’s parameters and those of the timing model, our model can bring about a factor 2.6 improvement on the measurement precision of the mass ratio, R = mA/mB, between the two pulsars: a theory-independent parameter, which is pivotal in tests of GR.

Numerical relativity simulation of GW150914 in Einstein-dilaton-Gauss-Bonnet gravity

A present challenge in testing general relativity (GR) with binary black hole gravitational wave detections is the inability to perform model-dependent tests due to the lack of merger waveforms in beyond-GR theories. In this study, we produce the first numerical relativity binary black hole gravitational waveform in Einstein dilaton Gauss-Bonnet (EDGB) gravity, a higher-curvature theory of gravity with motivations in string theory. We evolve a binary black hole system in order-reduced EDGB gravity, with parameters consistent with GW150914. We focus on the merger portion of the waveform, due to the presence of secular growth in the inspiral phase. We compute mismatches with the corresponding general relativity merger waveform, finding that from a post-inspiral-only analysis, we can constrain the EDGB lengthscale to be $\sqrt{\alpha_\mathrm{GB}} \lesssim 11$ km.

The missing link in gravitational-wave astronomy: discoveries waiting in the decihertz range

The gravitational-wave astronomical revolution began in 2015 with LIGO’s observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like laser interferometer gravitational-wave observatory (LIGO), Virgo and KAGRA will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based laser interferometer space antenna (LISA) will enable gravitational-wave observations of the massive black holes in galactic centres. Between ground-based observatories and LISA lies the unexplored dHz gravitational-wave frequency band. Here, we show the potential of a decihertz observatory (DO) which could cover this band, and complement discoveries made by other gravitational-wave observatories. The dHz range is uniquely suited to observation of intermediate-mass (∼102–104 M ⊙) black holes, which may form the missing link between stellar-mass and massive black holes, offering an opportunity to measure their properties. DOs will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing dHz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity (GR) and the standard model of particle physics. Overall, a DO would answer outstanding questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology.

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.