Gravitational Field Research Articles

Measuring gravitational attraction with a lattice atom interferometer.

Despite being the dominant force of nature on large scales, gravity remains relatively elusive to precision laboratory experiments. Atom interferometers are powerful tools for investigating, for example, Earth's gravity1, the gravitational constant2, deviations from Newtonian gravity3-6 and general relativity7. However, using atoms in free fall limits measurement time to a few seconds8, and much less when measuring interactions with a small source mass2,5,6,9. Recently, interferometers with atoms suspended for 70 s in an optical-lattice mode filtered by an optical cavity have been demonstrated10-14. However, the optical lattice must balance Earth's gravity by applying forces that are a billionfold stronger than the putative signals, so even tiny imperfections may generate complex systematic effects. Thus, lattice interferometers have yet to be used for precision tests of gravity. Here we optimize the gravitational sensitivity of a lattice interferometer and use a system of signal inversions to suppress and quantify systematic effects. We measure the attraction of a miniature source mass to be amass = 33.3 ± 5.6stat ± 2.7syst nm s-2, consistent with Newtonian gravity, ruling out 'screened fifth force' theories3,15,16 over their natural parameter space. The overall accuracy of 6.2 nm s-2 surpasses by more than a factor of four the best similar measurements with atoms in free fall5,6. Improved atom cooling and tilt-noise suppression may further increase sensitivity for investigating forces at sub-millimetre ranges17,18, compact gravimetry19-22, measuring the gravitational Aharonov-Bohm effect9,23 and the gravitational constant2, and testing whether the gravitational field has quantum properties24.

Constraining Variable Generalized Chaplygin Gas model in Matter Creation Cosmology

Abstract We explore the variable generalized Chaplygin gas (VGCG) model in the theory of matter creation cosmology within the framework of a spatially homogeneous and isotropic flat Friedmann - Lema\^{i}tre - Robertson - Walker space-time. Matter creation cosmology is based on reinterpretation of energy-momentum tensor in Einstein's field equations. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. The variable Chaplygin gas (VCG) is also studied as a particular solution. We use the Markov Chain Monte Carlo method to constrain the free parameters of three models, namely, $\Lambda$CDM, VGCG and VCG models with and without matter creation from the latest observational data from baryon acoustic oscillations, cosmic chronometer, type Ia supernovae (Pantheon) including gamma-ray burst, quasars, and the local measurement of $H_0$ from R21 data. Two different combinations of dataset provide a fairly tight constraint on the parameters of the $\Lambda$CDM, VGCG and VCG models. The present values of various cosmological parameters are obtained which give very close to $\Lambda$CDM model. Furthermore, we perform the stability analysis, Bayesian evidence analysis and information criteria analysis for these models through studying the sound speed, Bayes factor, and AIC and BIC selection criterion. The values of sound speed for VGCG and VCG models shows that both the models are stable. According to AIC, it is observed that VGCG and VCG models with matter creation are supported considerably less by current observations whereas BIC shows that these models are not favoured by observational data.

Manifest color-kinematics duality for point particles interacting with self-dual fields

We find that point particles interacting with a self-dual Yang-Mills field and self-dual gravity manifestly satisfy color-kinematics duality at the level of action. In a similar way color-kinematics duality also holds for a scalar field minimally coupled to a self-dual Yang-Mills field and self-dual gravity. By applying the appropriate limiting procedure to these scalar field theories we reproduce point particle theories we started from. This allows us to connect worldline color-kinematics duality to amplitude color-kinematics duality in field theory. Considering that point particles act as sources of classical solutions, our results may be regarded as a step towards establishing a precise relation between the amplitude and the classical double copies in the self-dual sector. Finally, we briefly mention that the extension of this discussion to the higher-spin case suggests that scalar point particles cannot interact with chiral higher-spin fields.

Infrared structures of scattering on self-dual radiative backgrounds

The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional celestial sphere. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level collinear splitting functions — or celestial OPEs — and infinite-dimensional chiral soft algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the MHV sectors of gauge theory and gravity.

Connecting the Brazilian Vertical System to the International Height Reference Frame by estimating the vertical datum parameters

One of the challenges in the unification of the global vertical datum is to determine the vertical offset between the local vertical datum and the global vertical datum. Since 2015, the scientific community has been working on the unification of the global vertical datum, following the publication of the resolution for the definition and realization of an International Height Reference System. This paper aims to estimate the vertical offset in Brazil (Imbituba and Santana Data) by combining a regional gravity field model, using the Geodetic Boundary Value Problem approach applying the Remove-Compute-Restore procedure, and GNSS/leveling data. In the Imbituba vertical datum 1271 stations were used and 66 stations were connected to the Santana tide gauge. The results showed that the geopotential value of Imbituba was 62,636,849.87 ± 0.224 m2s-2, and the vertical offset concerning the reference surface (W0) was 0.358 ± 0.023 m. In Santana, the geopotential value was 62,636,836.88 ± 4.108 m2s-2, and the vertical offset was 1.689 ± 0.420 m. The offset between Imbituba and Santana was computed once the physical connection between Brazil's two local vertical data is a challenge. The estimated value was 1.331 ± 0.421 m. This means the Santana vertical datum is 1.331 m higher than the Imbituba vertical datum.

Quenching of zonal winds in Jupiter’s interior

Gravity and magnetic field data obtained by the Juno mission show that Jupiter's strong zonal winds extend a few thousand kilometers into the interior, but are quenched above the level where the electrical conductivity becomes significant. Here, we extend a simple linearized model [Christensen et al., Astrophys. J. 890, 61 (2020)] that explains the braking of the jets by the combination of stable stratification and electromagnetic effects. We show that in the inviscid limit, the process is essentially governed by a single parameter, which we call the MAC-number (for the forces acting on the flow-Magnetic, Archimedian, and Coriolis). The predictions for the drop-off of the zonal winds agree well with results from 3D-convection models. We run calculations that take the full range of density and electrical conductivity variations in the top 5,600 km of Jupiter into account. In order to satisfy constraints on the power driving the jets and on their effect on Jupiter's magnetic field, the top of the stable layer and the region where the jet velocity drops sharply must be near 2,000 km depth. The dissipation associated with quenching of the jets increases toward the poles, which can partly explain why the jets near [Formula: see text]20[Formula: see text] are faster than those at higher latitude.

RTModel : Platform for real-time modeling and massive analyses of microlensing events

The microlensing of stars in our Galaxy has long been used to detect and characterize stellar populations, exoplanets, brown dwarfs, stellar remnants, and all other objects that may magnify the source stars with their gravitational fields. The interpretation of microlensing light curves is relatively simple for single lenses and single sources, but it becomes more and more complicated when we add more objects and take their relative motions into account. RTModel is a modeling platform that has been very active in the real-time investigations of microlensing events, providing preliminary models that have proven very useful for driving follow-up resources towards the most interesting events. The success of RTModel comes from its ability to carry out a thorough and focused exploration of the parameter space in a relatively short time. This modeling process is based on three key ideas. First, the initial conditions are chosen from a template library including all possible caustic crossing and approaches. The fits are then made using the Levenberg-Marquardt algorithm with the addition of a bumper mechanism to explore multiple minima. Finally, the basic computations of microlensing magnification are performed by the fast and robust VBBinaryLensing package. In this paper, we illustrate all the algorithms of RTModel in detail with the intention to foster new approaches in view of future microlensing pipelines aimed at massive microlensing analyses.

Assessment of Callisto Gravity-field Determination Using the Inter-satellite Range-rate Link

China will launch the “Tianwen-IV” mission around 2030, focusing on the orbiting exploration of Jupiter and Callisto, a moon of Jupiter. As part of this ambitious mission, a main satellite will carry another satellite that will be released in the Jupiter system to continue its journey toward Uranus. Considering the current mission planning, we propose an inter-satellite radio-observation mode that differs from the conventional observation mode of tracking from Earth to precisely determine the orbit of the satellites. Given the significance of the Callisto gravity field model in both science objectives and satellite navigation, we have conducted a series of simulation experiments to evaluate the potential of this inter-satellite range-rate data for accurately estimating the Callisto gravity field. The results obtained from the analysis demonstrate that by utilizing 40 days of ground station observations, it is possible to estimate the gravity field model of Callisto up to a degree of 70. Remarkably, when combining these ground station observations with inter-satellite observations, a comparable level of accuracy can be achieved with just 10 days of observations. Furthermore, with reduced inter-satellite observation noise, accuracy improves, enabling estimation up to 80 degrees or higher. Initial inter-satellite distance selection impacts estimation accuracy. These findings serve as a valuable test bed for the future “Tianwen-IV” mission to perform precise orbit determination and gravity field model estimation to reduce reliance on deep space stations.

Structural interpretation of the basement beneath the Southern Desert of Iraq based on aeromagnetic data

The Southern Desert (SD) of Iraq is located in the southernmost region of Iraq and is tectonically located on the stable part (proximal domain) of the Arabian Platform. The area is characterized by a considerable thickness of nonmagnetic Phanerozoic sediments overlying a reworked Proterozoic basement. Due to the intense nature of the karst near-surface geology, the basement has neither been seismically imaged nor drilled. In such situations, potential field (gravity and magnetic) exploration methods can often help to identify and map the deep structure of the basement. Here, the aeromagnetic field data, which cover all of the SD, are used to determine the structure and approximate depth of the basement. We use the combined results of the tilt derivative and phase preserving dynamic range compression (PPDRC) methods to qualitatively delineate the main basement structures and then use the source parameter imaging (SPI), tilt-depth (TD), and finite SPI (FSPI) methods to determine the basement depths. The qualitative interpretation of the tilt derivative and PPDRC methods identifies three north–south to northeast–southwest-trending linear negative anomalies that could represent extensional grabens in the basement surface. These grabens divide the basement into three blocks: the northwest block, the central block, and the southeast block. The magnetic anomalies over the basement blocks suggest that the northwest and central blocks are cut by a set of north–south to north-northwest–south-southeast and northeast–southwest faults. Depth estimation methods over the uplifted blocks have minimum depths between 4 and 5 km, whereas, over the graben, the depths range from 7 km to in excess of 12 km. The FSPI method, unlike the SPI and TD methods that use an infinite depth source body, gives depths generally deeper by up to 1.1 km if the assumed Curie-point depth is 21 km. A more realistic Curie-point depth of 32 km is used in the final interpretation model. These inferred basement blocks, grabens, and subbasin structures agree in general with the regional structures associated with the Arabian Peninsula and could provide an important framework for developing future hydrocarbon exploration strategies of the SD.

Black bounces in conformal Killing gravity

In this work, we analyse black bounce solutions in the recently proposed “Conformal Killing gravity” (CKG), by coupling the theory to nonlinear electrodynamics (NLED) and scalar fields. The original motivation of the theory was essentially to fulfill specific criteria that are absent in existing gravitational theories, namely, to obtain the cosmological constant as an integration constant, derive the energy–momentum conservation law as a consequence of the gravitational field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. In this work, we extend the static and spherically symmetric solutions obtained in the literature, and explore the possibility of black bounces in CKG, coupled to NLED and scalar fields. We find novel NLED Lagrangian densities and scalar potentials, and extend the class of black bounce solutions found in the literature. Furthermore, within black bounce geometries, we find generalizations of the Bardeen-type and Simpson–Visser geometries and explore the regularity conditions of the solutions.

Third‐Order Structure Functions of Zonal Winds in the Thermosphere Using CHAMP and GOCE Observations

AbstractWe use multi‐year observations of cross‐track winds (u) from the CHAllenging Minisatellite Payload (CHAMP) and the Gravity Field and Steady State Ocean Circulation Explorer (GOCE) to calculate third‐order structure functions in the thermosphere as a function of horizontal separation (s). They are computed using the mean (〈δu3〉) and the median and implemented over non‐polar satellite paths in both hemispheres. On height averages, 〈δu3〉 is shown to scale with s2 for s ≃ 80–1,000 km, in agreement with equivalent estimates in the lower atmosphere from aircraft observations. Conversely, follows an s3 power law for almost the whole s range, consistent with the two‐dimensional turbulence scaling law for a direct enstrophy cascade. These scaling laws appear independent of winds in distinct atmospheric regions. Furthermore, the functions are predominantly positive, indicating a preferential cyclonic motion for the wind.

Toward the Analysis of the Equation of Motion of a Ball Moving Unevenly in a Gravity Field

Toward the Analysis of the Equation of Motion of a Ball Moving Unevenly in a Gravity Field

Full Account of the Energy of the Gravitational Field in Cosmology and Spacecraft Ballistics

Full Account of the Energy of the Gravitational Field in Cosmology and Spacecraft Ballistics

Determining the difference between local acceleration and local gravity: Applications of the equivalence principle to relativistic trajectories

We show by direct calculation that the common equivalence principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is, therefore, possible, at least as a matter of principle, to tell the difference between local acceleration and a true gravitational field by measuring the local deflection of light. We calculate as well the deflection of test particles of arbitrary energy and construct a leading-order coordinate transformation from Schwarzschild to local inertial coordinates, which shows explicitly how the effects of spatial curvature manifest locally for relativistic trajectories of both finite and vanishing rest mass particles.

A Multipole Representation for the Gravitational Field of Asteroid (433) Eros

A Multipole Representation for the Gravitational Field of Asteroid (433) Eros

Spatial interpolation techniques comparison and evaluation: The case of ground-based gravity and elevation datasets of the central Main Ethiopian rift

The ground-based gravity data reveals diverse anomaly signatures in areas of the Main Ethiopian rift where active volcanic and tectonic activities are dominant. In such a region ground-based data collection is restricted to existing roads and relies on accessible stations. These resulted in gaps in data, either missing, uneven, or insufficient spatial coverage that must be estimated with proper interpolation techniques. Comparison and evaluations of the spatial interpolation methods that are commonly used in potential field geophysical data analysis were made for the terrestrial gravity and elevation data of the central Main Ethiopian rift. In this research, two widely used interpolation techniques, minimum curvature interpolation, and Ordinary Kriging were compared and assessed. A 10 % hold-out validation was employed, where 90 % of the data points were used to generate interpolated surfaces, which were then evaluated against the remaining 10 %. Following interpolation with each technique, the generated grid was converted into discrete data points (estimated values). These are then compared with the available gravity data, which were deliberately excluded from the gridding process (10 % remaining dataset). The accuracy of each method was assessed by evaluation metrics such as mean value, variance, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), correlation coefficient (r), and R-squared. The results showed that the ordinary Kriging interpolation method outperformed the minimum curvature interpolants for gravity data with all performance metrics, while both interpolants seem to perform equally well for the elevation dataset. Therefore, it is proposed to use the Kriging interpolation method for potential field gravity studies conducted in the central Main Ethiopia rift.

Regional evaluation of global geopotential models and three types of digital elevation models with ground-based gravity and GNSS/levelling data using several techniques over Sudan

Abstract To evaluate the performance of the global geopotential models (GGMs) in a more unbiased way, ground-based gravity and GNSS/levelling datasets are highly required. In this study, the eight latest releases of the satellite-only and combined GGMs are evaluated on the regional scale using the available terrestrial gravity and GNSS/Levelling data over Sudan, considering the spectral consistency issue by applying the spectral enhancement method (SEM). The evaluation process consists of three stages: firstly, the eight GGMs are evaluated globally with each other by using different degree variances in terms of geoid heights, gravity anomalies, and signal-to-noise ratio (SNR); secondly, the GGMs are compared against the Earth Gravitational Model 2008 (EGM2008) on a regional scale over Sudan; thirdly, apply the SEM strategy by incorporating high (SEM_WITHOUT_RTM technique) and very-high (SEM technique) frequencies of the gravity field spectrum from the EGM2008 and high-resolution residual terrain model (RTM), respectively. For reliable robustness of the latter evaluation process, three different DEMs are used, namely, SRTM30, ASTER30, and GTOPO30. Our findings on the evaluation process using SEM_WITHOUT_RTM technique show improved gravity anomalies solutions regarding differences of standard deviations (STD) from 19–20.7 mGal to about 14 mGal. When applying the SEM technique, more improvements are achieved, providing STD differences in gravity anomalies and geoid heights of about 12 mGal and 45 cm, respectively. Among the three applied DEMs, it has been found that despite the slight refinements, the ASTER30 and GTOPO30 models show better performance than the SRTM30 model.

Extremely compact sources (ECS): a new potential field filtering method

We present a new filtering method for potential fields, based on modelling the fields in terms of very compact solutions, i.e., the sources are expected to occupy the smallest allowable volume in the source domain. The selected solutions, which we call “Extremely Compact Sources” (ECS) form a sort of atomized model, which still satisfies the non-unique inverse problem of gravity and magnetic fields. The ECS model is not only characterized by sparsity, but also by large values of the physical property (density or magnetic susceptibility). The sparse nature of the model allows for the definition of a highly localized filter, which can be obtained by simply specifying the atoms to be selected in a given area. This feature allows managing tasks normally impossible with traditional filters, such as the separation of interfering anomalies having a similar wavenumber content. In addition, the procedure can perform a very effective regional/residual separation. We demonstrate the method on synthetic cases and apply it in the real case of gravity data of Campi Flegrei volcanic area (Italy), where we use the ECS filtering to isolate the gravity effect of the Mount Olibano dome.

Superconformal anomalies from superconformal Chern-Simons polynomials

We consider the 4-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Lie superconformal algebra and search for completely “symmetric” (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal a-anomaly. We briefly discuss the possibility that the superconformal c-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results.

Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion

We study a massless real self-interacting scalar field φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document} non-minimally coupled to Einstein gravity with torsion in (2+1) space-time dimensions in the presence of a cosmological constant. The field equations with a self-interaction potential V(φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varphi )$$\\end{document} including φn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi ^{n}$$\\end{document} terms are derived by a variational principle. By numerically solving these field equations with the 4th Runge–Kutta method, the circularly symmetric rotating solutions for (2+1) dimensions Einstein gravity with torsion are obtained. Exact analytical solutions to the field equations are derived for the proposed metric in the absence of both torsion and angular momentum. We find that the self-interacting potential only exists for n=6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=6$$\\end{document}, as requested by conformal symmetry. We also study the motion of massive and massless particles in (2+1) Einstein gravity with torsion coupled to a self-interacting scalar field. The effect of torsion on the behavior of the effective potentials of the particles is analyzed numerically.