Gravitational Field Research Articles

Revisiting the dynamics of a charged spinning body in curved spacetime

Abstract We analyze the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin condition for the body with the magnetic dipole moment proportional to spin, which generalizes the one proposed by Ohashi-Kyrian-Semerak for gravity. As a result, we get the whole family of charged spinning particle models in the 
 curved spacetime with remarkably simple dynamics (momentum and velocity are parallel). Applying the reparametrization procedure, for a specific dipole moment, we obtain equations of motion with constant mass and gyromagnetic factor. Next, we show that these equations follow from an effective Hamiltonian formalism, previously interpreted as a classical model of the charged Dirac particle.

Weighing the vacuum with the Archimedes experiment

Exploring the complex connection between vacuum fluctuations and gravitational field is the goal of Archimedes experiment. Tiny changes in the weight of the vacuum contained in high-temperature superconductors can be measured using a high-precision balance. These structures can absorb or expel vacuum energy depending on their normal or superconductive status. In the measurement, the state of the sample is modulated into two states, normal and superconducting, with a reversible transition achieved by periodically varying the temperature of the thermal bath. The paper provides the current status of the experiment, highlighting the study and construction of the balance with its thermal modulation and cryogenic systems, and the investigation of high-temperature superconductor candidates.

Charged particles in dipole magnetosphere of neutron stars: epicyclic oscillations in and off-equatorial plane

Abstract We study the motion of charged test particles around a magnetized neutron star described by the Schwarzschild gravitational field of mass M and a dipole magnetic field characterized by parameter b, representing the ratio of electromagnetic to gravitational forces. The neutron star’s radius is assumed at $$R=3M$$ R = 3 M . Circular orbits “in” and “off” the equatorial plane, determined by the dipole field’s symmetry plane, are analyzed based on background and particle parameters; their stability against radial and latitudinal perturbations is established. The existence of chaotic charged particle motion in belts around off-equatorial orbits, influenced by sufficiently strong repulsive magnetic force, is demonstrated. The belts’ distance from the neutron star varies with parameter b for different charged particles. Frequencies of epicyclic oscillatory motion related to “in” and “off” equatorial circular orbits, alongside the orbital frequency, are determined. The magnetically modified geodesic model is applied to fit observational data from twin-peak, high-frequency quasi-periodic oscillations in binary systems containing neutron stars. Rough fitting to the data for circular orbits for particles under magnetic attraction (repulsion) is shown. The possible fittings imply strong limits on the magnetic parameter, $$b \sim 0.01$$ b ∼ 0.01 ( $$b \sim -10$$ b ∼ - 10 ) for magnetic attraction (repulsion), suggesting minor influence of electromagnetic forces and test particles with small specific charges like dust or plasmoids in strong magnetic fields around neutron stars.

Would the 2021 Western Europe Flood Event Be Visible in Satellite Gravimetry?

AbstractThe primary objective of the GRACE Follow‐On satellite mission is to measure temporal changes in the Earth's gravitational field. Distance variations between the two GRACE‐FO satellites, recorded by a K‐Band Ranging system and a new Laser Ranging Interferometer (LRI), are significantly influenced by atmospheric mass redistribution. We investigate whether the sub‐monthly variations in atmospheric water mass, precipitation, and changes in total water storage during the extreme flood event in western Europe in 2021 were sufficiently large to influence the satellite gravity field measurements, if the GRACE‐FO satellites would have passed directly over the region. We use several data sets such as weather forecasts (ICON‐D2 model), hydrological simulations (ParFlow/CLM), observations as well as reanalyses, showing the high uncertainty between different estimations of the considered variables: total precipitable water, total precipitation, and total water storage. Our estimates suggest a potentially noticeable impact of the 2021 flood event on the GRACE‐FO satellites. Although it was globally seen a rather small event, even the atmospheric water mass beyond water vapor, which is not considered within the de‐aliasing process, is close to the LRI detection accuracy. This is particularly relevant for future gravity missions, which will use the LRI with potentially higher sensitivity as their main instrument. Sub‐monthly variations in the total atmospheric water mass, that is, beyond water vapor of huge extreme precipitation events should be investigated further to reduce potential future aliasing errors.

Exhibiting stable model of dark energy compact star with Tolman-VI solution under complexity free system

Several recent developments have highlighted the significance of the vanishing complexity factor formalism in understanding the structure and evolution of stellar relativistic compact objects. This formalism, introduced through a novel definition proposed by Herrera (Phys. Rev. D 97:044010, 2018), offers valuable insights into the dynamics of such systems. In this manuscript, we explored a class of realistic solutions to the static and spherically symmetric field equations characterized by two fluid distributions: ordinary stellar matter and dark energy, within the framework of this formalism. Utilizing the well-known Tolman-VI solution as the seed ansatz for the metric coefficient grr, we employed the complexity-free format to derive an analytic solution for the other metric coefficient, gtt. Subsequently, we obtained the solutions of gravitational field equations for our proposed spacetime model by incorporating the linear dark energy equation of state. These results were applied to the astrophysical compact star candidate LMC X-4, with M=1.04M⊙ and R=8.4km. The potential viability and credibility of the proposed dark star solutions were thoroughly analyzed by examining key constraints, including the regularity of metric functions, physical adequacy through matter variables, state parameter behavior, energy conditions, stability tests (such as pressure anisotropy and hydrostatic equilibrium), the speed of sound, and the mass–radius relation for this compact star candidate. Notably, the estimated values of the dark energy coupling factor, presented in Table 1, highlight the exotic nature of the fluid distribution and effectively quantify the contribution of dark energy to the structure and evolution of an ultra-relativistic dark compact star. These findings strongly support our model solutions and demonstrate improvements over previously reported results in Rej et al. (Chin J Phys 87:608, 2024).

Spatial-domain combination of GRACE monthly time-variable gravity models based on multiple weighting strategies and comparison of models’ performance in the Caspian Sea

The Gravity Recovery and Climate Experiment (GRACE) mission provides original observations to different institutions for the production of various monthly time-variable gravity field models (TVGFMs). Aiming to optimize the signal-to-noise ratio of TVGFMs, we determine to combine them in the spatial domain. This combination comprises two approaches: one combines spherical harmonic coefficient (SHC) solutions, and the other combines SHC and mascon (mass concentration) solutions together. For each approach, we employ four old weighting schemes and one new scheme named oceanic accuracy weighting. We then assessed the combined models through both internal and external validations. In external validation, we compare the Caspian Sea level changes derived from the combined models with those obtained from satellite altimeter. Our results reveal an improvement of the SHC combination using variance component estimation (VCE) weighting compared to any single SHC solution. Moreover, we found enhanced performance in the combined models with the incorporation of mascon solutions, particularly employing the oceanic accuracy weighting. These findings underscore the efficacy of model combination in improving performance, and emphasize the importance of selecting appropriate weighting strategies for integrating GRACE solutions. Specifically, we recommend VCE weighting scheme for combining SHC solutions only and oceanic accuracy weighting scheme for integrating mascon and SHC solutions.

New insights into the crustal structures of the Arabian Plate and surrounding plates unveiled from the crustal thickness model and its implications for geodynamics

Geodynamics of the Arabian Peninsula is less understood as crustal structures are not well delineated due to uneven distribution and lack of seismic measurements and ground based geophysical data in the Arabian interior. To address this, we delineated crustal structures in the Arabian Peninsula through the creation of a crustal thickness model from the inversion of GOCO60s gravity field model, which revealed details on the underlying crustal structures. Our model revealed strong crustal thickness variations in the Zagros fold belt that indicates high deformational history and crustal reworked, which also reflect directional collisional events between the Arabian and Eurasian Plates, similar to the Himalaya type as the result of mantle processes. The resolved crustal structures also reveal a relatively slow rifting process on the southern end of the Red Sea than at the northern end, which resulted in the bulging of crust in the southern part of Zagros Fold Mountains. Further, folding and bulging of crustal structures is more intense near the Arabian Platform and slower on the Eurasian side, which could indicate a relatively stable Eurasian plate compared to the geodynamically active Arabian Plate. Overall improvement in our high-resolution crustal thickness model yields an improved representation of crustal structures over previously derived models of the Arabian Peninsula and the Surrounding plates that indicates a variation in the Proterozoic crust in Arabian Plate, possibly indicating a secular variation in the crustal structure.

Connection of the Theory of Time with the Friedmann Equation

The proposed work shows a new approach to deriving the Friedmann equation. The approach is based on the fact that the primary medium from which the universe could arise is a time substance consisting of primary tiny particles. This medium is described by a scalar field. The mathematical apparatus used for its study allowed obtaining dual equations, which were interpreted by the author as waves of direct and reverse time directed towards each other. When the waves contacted, an inversion of the reverse wave occurred. It took the direction of the direct wave. As a result of the inversion, dynamic processes arose that led to the appearance of acceleration in 4-dimensional space. Analysis of the formulas for velocity and acceleration led to the derivation of Friedmann equations for a flat universe, obtained by him from Einstein's gravitational equation. Introduction. The concept of a continuous space-time continuum has become firmly established in modern physics. It was introduced by A. Einstein in the special and then General Theory of Relativity (GTR). By tacit agreement, it is generally accepted that the continuum is filled with matter that is in continuous motion, moving at speeds not exceeding the speed of light. Matter has mass, which leads to the curvature of space-time. GTR interprets this curvature as the presence of a gravitational field in the continuum. To describe it, A. Einstein's tensor gravitational equation is used. It is used to analyze curved 4-dimensional space-time. With this approach, the dimension consists of three spatial and one time coordinate. The result is a mathematically complex theory, lacking clarity and poorly understood. In 1922, A.A. Friedman solved the equations of GTR after modifying the second cosmological postulate. This led to a result that meant a change in the size of the Metagalaxy over time, i.e. to its non-stationarity. The solutions obtained formed the basis of the theoretical basis of cosmology. No other approaches to deriving Friedman's equations, except on the basis of GTR, were undertaken. But there is another approach. And the author talks about it in this article. It is based on the theory of time developed by him.

Correction of global elevation data SRTM to the national elevation system in the territory of Vietnam

This paper presents a five-step procedure for correcting the global elevation data Shuttle Radar Topography Mission (SRTM) to the national elevation system involving: (1) selecting GNSS/levelling points, obtaining global elevation data SRTM from https://earthexplorer.usgs.gov/ and height anomalies of the global gravity field model EGM96 from http://icgem.gfz-potsdam.de/home, corresponding to GNSS/levelling points; (2) calculating the deviation between the global elevation data SRTM and the measured height of GNSS/levelling points; (3) converting the global elevation data SRTM to national elevation; (4) checking the global elevation data SRTM after converting to national elevation; and (5) performing correction and evaluation. The procedure is carried out on the territory of Vietnam from 813 GNSS/levelling points of grades I, II and III. The results show that the accuracy before and after correction is ±4.112 m and ±3.131 m, respectively, for the territory of Vietnam, >3 m and >2 m for mountainous regions including Northwest, Northeast, North Central, South Central, Central Highlands and Southeast, where the elevation ranges from 700 to 1500 m, and from <3 m to <2 m for plain regions including Red River Delta, Southwest, where the elevation ranges from 2 to 10 m. The correction results of the global elevation data SRTM based on GNSS/levelling points indicate that the accuracy before and after correction depends on the topographical characteristics. These correction results for eight different regions in Vietnam are also consistent with research conducted in various regions of the world.

Interior and Gravity Field Models for Uranus Suggest a Mixed-composition Interior: Implications for the Uranus Orbiter and Probe

Interior and Gravity Field Models for Uranus Suggest a Mixed-composition Interior: Implications for the Uranus Orbiter and Probe

Enhancing Mars Gravity Field Solutions with China’s Tianwen-1 Tracking Data

Abstract The Tianwen-1 (TW1) mission, which successfully entered Mars's orbit in 2021, provides a valuable data set for enhancing the understanding of Mars’s gravity field. The highly elliptical near-polar orbit of the TW1 orbiter offers unique sensitivity to long-wavelength gravity signals, complementing the contributions of low-altitude missions like the Mars Reconnaissance Orbiter (MRO). In this study, we used 4 months of TW1 radio tracking data in combination with MRO data to develop a new Mars gravity field model up to degree and order 50. We evaluated the improvement of gravity field determination through power spectrum analysis, gravity anomaly maps, and trajectory precision assessment. The result shows significant improvements in accuracy up to degree and order 30, with an average enhancement of 38% in the zonal harmonic coefficients. There are obvious differences between the two gravity field models in gravity anomaly maps. The range of gravity anomaly errors improves after incorporating TW1 data, with the maximum error decreasing from 53.4 to 46.4 mGal and the average error improving from 8.4 to 7.3 mGal. Additionally, orbit determination experiments confirm that the fused gravity field model enhances trajectory modeling for both MRO and TW1. These findings highlight the scientific value of TW1 tracking data in advancing Mars’s gravity field modeling and provide critical insights for future deep-space missions.

Test particles in Kaluza–Klein models

Abstract Geodesics in general relativity describe the behaviour of test particles in a gravitational field. In 5D Kaluza–Klein, geodesics reproduce the Lorentz force motion of particles in an electromagnetic field. This paper studies geodesic motion on a higher-dimensional M 4 × K with background metrics encoding general 4D gauge fields and Higgs-like scalars. It shows that the classical mass and charge of a test particle become variable quantities when the geodesic traverses regions of spacetime with massive gauge fields, such as the weak force field, or with non-constant Higgs scalars. This agrees with the physical fact that interactions mediated by massive bosons can change the mass and charge of particles. The variation rates of mass and charge along a geodesic are given by natural geometric formulae. In regions where mass is preserved, there are additional constants of motion, one for every abelian or simple summand in the Killing algebra of K. The last part of the paper discusses traditional difficulties of Kaluza–Klein models, such as the low q / m ratios in the 5D model. It suggests possible ways to circumvent them. It also remarks the naturalness of a model in which elementary particles always travel at the speed of light in higher dimensions.

Relating Madelung–Bohm trajectories

In this work, we use the quantum potential approach to quantum mechanics to show that the Madelung–Bohm trajectories for a particle in a constant gravitational field can be related to those of a free particle by means of a quantum point transformation defined in the extended configuration space. We find that the point transformation also gives a connection between the corresponding quantum Hamiltonians determined by the solutions of the corresponding Schrödinger equations for these two problems. We show that the Madelung–Bohm trajectories determined by the stationary solutions to the Schrödinger equation for the particle in a constant gravitational field are straight ones, while the corresponding ones for the free particle are parabolic trajectories. The Airy beam is one example of this type of solution. We study the properties of a solution to the Schrödinger equation for a free particle with phase singularities (zeroes), and we find that the corresponding solution to the Schrödinger equation for the particle in a constant gravitational field also has zeroes at the same spacetime points. However, the Madelung–Bohm trajectories determined by the two solutions are totally different. Furthermore, we remark that similar results can be directly obtained for the paraxial wave equation.

Machine learning web application for predicting varicose veins utilizing global prevalence data.

This study aimed to develop a web-based machine learning (ML) model to predict the lifetime likelihood of developing varicose veins using global disease prevalence data. We utilized data from a systematic review, registered under PROSPERO (CRD42021279513), which included 81 studies on varicose vein prevalence across various geographic regions. The data used to build the ML model included disease prevalence as the outcome (%), along with the following predictors: mean age, gender distribution (%), mean body mass index (BMI) of the study cohort, and the mean gravity field of the study region (mGal), representing variations in Earth's underground mass distribution that influence blood and fluid redistribution in the human body, affecting disease prevalence. After standardizing the outcome and predictors, the model was trained using neural network regression implemented with the TensorFlow.js library and deployed as a web-based ML application. After 406 epochs of training, and upon achieving a validation loss (mean squared error) of 0.9, training was stopped due to no further improvement. The achieved test loss was 0.49, and the mean absolute error (MAE) was 0.56, corresponding to an up to 6.7% difference between the predicted and true disease probabilities (calculated as MAE x σ, where σ is the standard deviation of the mean disease prevalence = 0.56 x 11.9 = 6.7). The likelihood of developing varicose veins, as predicted by the model, showed the strongest correlation with age (0.78), followed by gravity anomaly (0.30), BMI (0.27), and gender (0.15). This study summarizes research on the prevalence of varicose veins by developing a web-based ML model to predict an individual's likelihood of developing the disease. Using data reported in the literature, the ML algorithm provides a non-discriminatory predictive baseline, offering a valuable tool for future investigations into disease epidemiology.

Identifying geological structures in the Pamir region using non-subsampled shearlet transform and gravity gradient tensor

Summary The Pamir tectonic zone originates from the intense collision of the Indo-Eurasian plate. Identifying the faults in the Pamir region region is essential for elucidating the collision mechanism and seismic characteristics. This paper compares the effect of the two-dimensional discrete wavelet transform (DWT2D) and the non-subsampled shearlet transform (NSST) on gravity field separation through synthetic model gravity field experiments. The results show that NSST can avoid the Gibbs phenomenon of DWT2D and better maintain the gravity field distribution. The surface gravity disturbances data of the Global Gravity Model Plus (GGMplus) with a high-spatial resolution (7.2 arcsec or approximately 200 m) is employed to separate the region-residual gravity fields in the neighbouring domain of the Pamir region based on the NSST. Furthermore, the gravity gradient tensor (GGT) is computed, and the correspondence between the GGT and the location and strike of the surrounding faults is analyzed. The results show that the GGT component and its various combinations can effectively identify shallow and deep faults, the residual field GGT and its combinations can effectively identify the distribution and direction of shallow faults, and the regional field GGT and its combinations can effectively identify the distribution and direction of deep faults. The existence of north-south trending faults in the Pamir-Hindu Kush region is widely accepted. However, our study has revealed an east-west trending concealed fault in the deep areas of the Hindu Kush (Depth &amp;gt; 200 km). This finding provides significant insights for studying the bidirectional subduction of the Indian and Eurasian plates. This research not only helps us to analyze the tectonic characteristics of the shallow and deep parts of the region separately but also provides complementary information for investigating the distribution of deep underground faults, especially when fault inversion of intermediate to deep source earthquakes is limited by factors such as uncertainty in source depth and complexity of seismic wave velocities.

Accounting for the expansion of the universe using an energy/momentum model to construct the space-time metric

Background The success of the theories of special and general relativity in describing localised phenomena, such as objects undergoing high speed motion or located in gravitational fields, needs no further elaboration. However, when applied to the evolution of the universe several problems arise which can require an additional model, e.g., inflation during the early expansion, and adjustments to parameters to account for phenomena such as the late-time acceleration of the universe. Methods Focusing on the difference between the ways in which space and time are measured, this paper shows that there are two paths which allow the equations of special relativity to be produced from the same basic postulates. Results Both the standard theory and the energy/momentum, or dynamic model, utilise the Minkowski metric, but with different coordinate systems. The dynamic model transforms Cartesian coordinates into an Euclidean form by multiplying the coordinates by functions of γ (= (1– ν 2/c 2)-1/2). When utilising these coordinates, the relativistic equations are unchanged for local phenomena such as the Lorentz coordinate transformation and the energy/momentum equation for high-velocity objects. Conclusions However, the derived coordinates alter the perceived overall structure of the universe in a manner that, for the simplest model under this system, allows the reproduction of observed cosmological features, such as the intrinsic flatness of the universe and the apparent late-time acceleration of its expansion, without the need of additional models or changes in parameter values.

The outer structure of old star clusters in the Small Magellanic Cloud

Abstract We report results on the internal dynamical evolution of old star clusters located in the outer regions of the Small Magellanic Cloud (SMC). Because the SMC has been imprinted with evidence of tidal interaction with the Large Magellanic Cloud (LMC), we investigated at what extend such an interaction has produced extra tidal structures or excess of stars beyond the clusters’ tidal radii. For that purpose, we used the Survey of the Magellanic Stellar History (SMASH) DR2 data sets to build number density radial profiles of suitable star clusters, and derived their structural and internal dynamics parameters. The analysed stellar density profiles do not show any evidence of tidal effects caused by the LMC. On the contrary, the Jacobi volume of the selected SMC star clusters would seem underfilled, with a clear trend toward a smaller percentage of underfilled volume as their deprojected distance to the SMC centre increases. Moreover, the internal dynamical evolution of SMC star clusters would seem to be influenced by the SMC gravitational field, being star clusters located closer to the SMC centre in a more advanced evolutionary stage. We compared the internal dynamical evolution of SMC old star clusters with those of LMC and Milky Way globular clusters, and found that Milky Way globular clusters have dynamical evolutionary paths similar to LMC/SMC old star clusters located closer to their respective galaxy’s centres. Finally, we speculate with the possibility that globular clusters belonging to Magellanic Clouds like-mass galaxies have lived a couple of times their median relaxation times.

Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity

In this work, we analyze various phenomena influenced by the gravitational field in a bumblebee gravity solution, with a particular emphasis on a traversable wormhole for massless particle modes. Specifically, we calculate the index of refraction, group velocity, time delay, modified distances, and interparticle potential, demonstrating the possibility of photon-photon interactions due to the wormhole geometry. For the latter aspect, we also extend the analysis to massive particle modes, resulting in a “combination” of modified Yukawa- and Coulomb-like potentials. These calculations are shown to be dependent on the wormhole’s parameters, particularly the wormhole throat. In addition to these analyses, the Hawking temperature is derived using the trapping horizon method, yielding negative values. Furthermore, we derive the thermodynamic properties of photon-like modes by incorporating the modified dispersion relation arising from the wormhole geometry, focusing on non-interacting particle modes. Remarkably, all calculations are conducted in a fully analytical framework.

On estimations of Dawn spacecraft’s capture probability into 1:1 ground-track resonance around Vesta

Abstract This paper develops semi-analytical and analytical methodologies to estimate the probability of the Dawn spacecraft being captured into a 1:1 ground-track resonance around Vesta. The spacecraft, using low-thrust propulsion, approached the asteroid Vesta, and one significant challenge during this phase is crossing ground-track resonances with the asteroid. As the capture phenomenon is dependent on the initial condition of the trajectory, it is necessary to accurately estimate the probability of such a capture. Firstly, the system dynamics are described by a model incorporating Hamiltonian perturbations from the irregular gravitational field up to the second degree and order, and continuous low-thrust that is constant in magnitude and directed in the opposite direction of the spacecraft’s velocity. The resonance region is enclosed by separatrices which are approximated with a fourth-order polynomial for quantitative analysis. The Hamiltonian, serving as a proxy for the system’s energy, changes when the spacecraft crosses the separatrices, and these changes are quantified using a global adaptive quadrature method. Finally, the probability of capture into ground-track resonance is estimated based on the energy change across the separatrices, and the accuracy and efficiency of the developed semi-analytical and analytical methodologies are investigated by comparing them to numerical simulations based on the perturbed Hamilton’s equations of motion. This research makes a significant contribution to the field of astrodynamics by providing a systematic and efficient approach to estimating the probability of resonance capture.

Critical parameters and equilibrium profiles for gravitational collapse with shear viscosity

Abstract In this letter, we investigate the instability around equilibrium of a poor thermal conductor with shear viscosity. The analytical formulation departs from a Boltzmann relation satisfied by the non-homogeneous density. The equilibrium condition together with the equation of state provide rescaled frequency, time, and viscosity. A viscosity parameter is then suitably identified. We find the radial profiles for the gravitational field and potential, and density at equilibrium. As a result, we obtain the critical radius and mass of the collapsing self-gravitating gas cloud as functions of the viscosity parameter. We find that shear viscosity cannot drive gravitational collapse of compact objects. Applications of our theory as a benchmark test for astrohydrocodes are addressed.