Gravitational Field Research Articles

Modeling the Impact of Greenland Ice Sheet Melting on Global Sea Level Elevation and Climate Change Feedback Mechanisms

The rapid acceleration of global warming is leading to an increased rate of glacier melt at the Earth's poles, which exacerbates the threats posed by the climate crisis and contributes to rising ocean levels. The Greenland Ice Sheet, recognized as the second-largest ice sheet globally, has housed its extensive glaciers and ice caps for at least 18 million years [1]. The melting and potential collapse of this ice sheet could significantly affect Worldwide climate and sea height. This research aims to develop a coupled model to assess rising sea levels caused by the thawing of the Greenland Ice Sheet, incorporating factors such as global warming, glacier volume, hydrothermal expansion, isostatic rebound, ice dynamics, changes in the gravitational field, and the absorption and release of methane gas. Additionally, the paper investigates the hazards connected to melting glaciers exacerbating global warming. This research provides a crucial foundation for forecasting the long-term impacts of the Greenland Ice Sheet's melting on global climate change.

A Study of the Doppler Effect in the Analysis of Black Hole Images

Black holes, one of the most mysterious objects in the universe, have long captured the attention of the scientific community due to their extreme gravity and intricate physics. In theory, a black hole is formed when a massive star or object collapses at the end of its life cycle. When a star exhausts its core energy and is no longer acted upon by external forces, it begins to collapse inward. This process continues until the star reaches a critical density, at which point its gravity becomes so strong that not even light can escape, forming a black hole. Black holes exert a profound influence on the universe, continuously absorbing matter in their vicinity, including gas, dust, and other celestial objects. Focusing on the core physical properties and related phenomena of black holes, this paper explores the profound impact of black holes on existing physical theories. By analyzing the motion of matter and energy release mechanism under the gravitational field of black holes, it reveals the complex dynamic behavior of black holes under extreme conditions. In addition, it emphasizes the existence of singularities and their challenges to physics theories, especially the limitations of quantum gravity theory. The study of the Doppler effect and the relativistic beam effect provides further evidence of the high-speed motion of the matter around a black hole and the changes in its radiation properties. These in-depth discussions provide new perspectives for understanding the quantum properties of black holes and their importance in astronomy.

Gravitation as a Statistical Theory on the Light Cone

Abstract In this paper, we will explore Padmanabhan’s mesoscopic, statistical approach to gravity [62] with a twist. The general picture of his approach is that spacetime is made of large numbers of localized quantum degrees of freedom. Padmanabhan assumed that the degrees of freedom of a given quantum state of geometry contribute, after averaging over fluctuations, a vector degree of freedom for spacetime at a point. For null vectors, this can be regarded as corresponding to one single vector, i.e. a pure state, for the statistical ensemble on the light cone at every point. In the present paper, we consider instead the case where the states of the gravitational degrees of freedom are spread out and overlap, with only probabilistic information on which of them determines the actual spacetime at a point. In the continuum limit, this corresponds to a mixed state for the statistical ensemble on the light cone at every point.

This change in assumptions leads to some interesting observations. When we define a statistical ensemble on the light cone, its variance ``knows'' about the interior of the light cone. As an intriguing consequence, we find that the cosmological constant can be related to the variance over the light cone.

With a mixed state, we can no longer derive the gravitational field equations from an entropy functional. Here, instead, we show that a naive implementation of the measure of a mixed state on the light cone in the variation principle leads to modified measure theories (MMT) as the grand canonical ensemble and allows one to reframe unimodular gravity as the canonical ensemble of a statistical theory on the light cone.

The physical nature of the event horizon in the Schwarzschild black hole solution

Abstract This study explores the relationship between the Schwarzschild metric and alternative metrics used to describe the gravitational field of a black hole in free space. While it is well-established that an infinite number of coordinate systems can be employed in general relativity, we demonstrate that the black hole solution is unique when expressed in a physically meaningful (proper) coordinate system. Notably, this coordinate system differs from the Schwarzschild metric due to the distinction between the true physical distance R and the Schwarzschild coordinate distance r. Consequently, the event horizon, commonly associated with the Schwarzschild solution, is shown to be a coordinate artefact of the chosen covariant metric tensor rather than a coordinate-invariant physical feature. As a result, no boundary prevents outgoing photons from escaping the black hole’s vicinity. This finding challenges the mainstream interpretation but remains fully consistent with general relativity. Moreover, it is supported by numerical modelling of light rays near a black hole. By reconsidering the existence of event horizons, this work offers potential resolutions to long-standing issues in black hole formation theories and the emission of electromagnetic and gravitational waves from black holes. Graphical abstract

The Orbits of Uranus, Its Satellites and Rings, the Gravity Field of the Uranian System, and the Orientation of the Poles of Uranus and Its Satellites**©2024 California Institute of Technology. Government sponsorship acknowledged.

Abstract R. A. Jacobson determined the orbits of the Uranian satellites, the masses of Uranus and its satellites, and the orientation of the pole of Uranus from Earth-based astrometry, Earth-based ring occultations, and observations acquired with the Voyager 2 spacecraft. Subsequent to that publication, several observers obtained new astrometry, and some of the original astrometry was rereduced against the Gaia star catalog. Moreover, R. G. French et al. made a new determination of the orbits of the Uranian rings, the orientation of the Uranian pole, and the gravity harmonics of Uranus from the entire set of Uranian ring occultations. Here we report the results of an analysis that redetermined the Uranus and satellite masses, satellite orbits, and the orbit of Uranus. In addition, we obtained a value for the Uranus tidal dissipation factor and produced an independent determination of the Uranian ring orbits, Uranus pole direction, and Uranus gravity harmonics. We also developed new expressions for the orientations of the satellites. We processed all of the data from our previous work plus the new and rereduced astrometry and the ring occultations. We extended our data arc forward to 2016 and backward to 1847. Our new orbit for Uranus is an update of that in ephemeris DE440 incorporating the occultation data and Gaia astrometry.

Lagrangian formalism in the theory of relativistic vector fields

The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its derivatives are directly involved. The obtained results, including equations for metric, equations of motion, and equations for fields, are applied to purely vector fields. As a consequence, formulas are determined for calculating the basic quantities necessary to describe physical systems. In this case, not only the pressure field and acceleration field are taken into account, but also the electromagnetic and gravitational fields outside the matter, which contribute to the four-momentum and to the four-dimensional angular momentum pseudotensor of each system. Each of the presented fields, including the gravitational field, has its own four-potential and its own tensor, which allows all calculations to be performed in a covariant way. In particular, when applying the principle of least action, the optimal approach is one in which the four-currents, field four-potentials and metric tensor depend on the observation point and vary independently from each other. In addition to the Euler–Lagrange equation, another equation of motion is derived containing the density of generalized four-force and the time derivative of the volume density of the generalized four-momentum. In order to uniquely calibrate the energy, which is a scalar quantity, the cosmological constant included in the Lagrangian is used. This leads to the fact that both the scalar curvature and the cosmological constant disappear in expression for the four-momentum of the system. In addition, the equation for the metric is simplified. The peculiarity of the equation for the metric is that the total stress-energy tensor of the physical system, presented in the right part of the equation for the metric, is associated only with field tensors and does not depend on particle four-velocities. Moreover, the trace of stress-energy tensor is zero. To calculate the stress-energy tensor, the functional derivative of Lagrangian density with respect to the metric tensor is used. The covariant derivative of stress-energy tensor leads to the equation of particle motion under the action of fields, and to the generalized Poynting theorem. The contractions of the field tensors with the Ricci tensor are equal to zero, so that each field makes its own contribution to the curvature of spacetime in the system. The inertial mass of a system is defined as the value connecting the four-momentum and four-velocity of the center of momentum of the system, and can be calculated using the square of the four-momentum. It is shown that the canonical representation of the angular momentum pseudotensor is its representation with covariant indices. The radius-vector of the center of momentum of a physical system is determined in covariant form.

Local existence of a classical solution to the Einstein–Maxwell–Klein–Gordon system in higher dimensions

In this paper, we study the local existence of a classical solution to the coupled Einstein and Maxwell–Klein–Gordon system in higher dimensions. This system provides a toy model to study the dynamics of the complex scalar fields under the influence of the interaction of the gravitational and electromagnetic fields. In the starting point, we introduce the metric of the space-time in the Bondi coordinate. Then, we construct the evolution equation in the form of a single first-order nonlinear integro-differential equation. Furthermore, we show that there exists a unique fixed point that is the solution of the main problem based on the contraction mapping arguments. Finally, for a given initial data, we prove the existence of a local classical solution.

A Way of Decoupling the Gravitational Bulk Field Equations of Regular Braneworld Black Holes to Suppress the Bulk Singularities

A Way of Decoupling the Gravitational Bulk Field Equations of Regular Braneworld Black Holes to Suppress the Bulk Singularities

Trajectories of Light Beams in a Kerr Metric: the Influence of the Rotation of an Observer on the Shadow of a Black Hole

This paper investigates the trajectories of light beams in a Kerr metric, which describes the gravitational field in the neighborhood of a rotating black hole. After reduction by cyclic coordinates, this problem reduces to analysis of a Hamiltonian system with two degrees of freedom. A bifurcation diagram is constructed and a classification is made of the types of trajectories of the system according to the values of first integrals. Relations describing the boundary of the shadow of the black hole are obtained for a stationary observer who rotates with an arbitrary angular velocity about the axis of rotation of the black hole.

Tectonics of Cauvery basin (India) in onshore and offshore portions

Morphometric studies coupled with geophysical investigations from petroliferous basins provide valuable information about tectonics of the regions. We deduce six morphologic parameters from the River Cauvery's designated (sub)watersheds and perform dendrogram clustering analysis. The main channels of the (sub)watersheds showcase steeper gradient and meandering nature with less concavity. On the other hand, the distributaries portray lesser gradient and straight nature with greater concavity. From the offshore region of the Cauvery basin, we perform gravity modeling. The results show variations in gravity values from low to high, -150 to 50 mGal probably because of the basement ridge-depression features. This anomaly orientation indicates the extension of the sub-basin in the region. A strong NE-SW gravity trend possibly suggests a high-density plug at mid-crust. The low gravity values near the Vedaranyam region indicate low-density rocks within the basement. Places of high gravity anomaly show a decrease in bathymetry depth and vice versa. This indicates isostatic compensation of the Moho geometry, possibly due to crustal thinning in the offshore areas. Isostatic regional gravity fields are manifested by Moho relief and can have implications on the lithospheric mechanical strengths. Bathymetric studies indicate multi-directional slopes. Relatively flat areas can indicate depocenters. E-W trending lineaments mapped on the Precambrian basement from a portion of the study area is presumably a manifestation of Cauvery Shear zone, which also persists in the offshore region.

How a Cosmology of a Nonlocally Unified, Meaningfully in-formed, Holographically Manifested and Purposefully Evolving Universe Engenders Planetary Systems as Gravitational Environments for the Emergence of Biological and Biomechanical Complexity

The emergent cosmology of a nonlocally unified, meaningfully in-formed, holographically manifested and purposefully evolving Universe, treats gravity as an emergent consequence of the in-formational and holographic nature of space-time and describes it as the consequence of the informational content, or intropy, associated with positions in space-time of massive bodies. In doing so, the evolutionary impulse inherently embodied in the Universe’s finite lifecycle engenders solar systems and planetary homes for the eventual evolution and complexity of biological organisms. Showing that planetary gravitational fields are required to enable cellular differentiation and subsequent development of a range of biomechanical strategies for building complex morphology, describes how such complex organisms such as human beings could eventually develop

Проблема создания трехмерных плотностных моделей геологических объектов на основе решения двумерной задачи гравиметрии: (Рецензия на статью М.Д. Сидорова, Ю.П. Трухина «Глубинное строение и металлогенический потенциал южного фланга Кувалорогского интрузивного массива (Камчатка)»)

Gravitational field inversion technologies aimed at creating three-dimensional detailed models of the real geological environment are constantly being improved, but the basic principles of solving inverse problems remain unchanged, violation of which does not allow obtaining a geologically meaningful result. The method of forming three-dimensional density models of the environment, presented in the article by M.D. Sidorov and Yu.P. Trukhin, as well as in other works of the authors, raises a number of questions, of which the main and fundamental is the correctness of the application of 2D density modeling in the study of a three-dimensional geological object. The legality of the transition from two-dimensional to three-dimensional models needs to be confirmed by simulation modeling. The absence of such constructions leads to the production of typical «compensation» sections that are inadequate for the real density distribution. Another aspect is the degree of detail of the resulting 3D model of the environment, compiled from the results of 2D modeling, which, of course, depends on the detail of the initial gravitational field. The quality and reliability of the results obtained should be confirmed by solving the direct 3D gravimetry problem from the created model of the medium.

Spinning up the spool: massive spinning fields in 3d quantum gravity

Spinning up the spool: massive spinning fields in 3d quantum gravity

On the classical limit of the (sub)n-leading soft graviton theorems in D = 4 without deflection

Tree-level gravitational amplitudes satisfy an infinite hierarchy of soft factorization theorems. The existence of these theorems has been recently linked with the existence of an infinite tower of asymptotic symmetries. In this paper, we analyze the relevance of the soft graviton theorems beyond sub-leading order in the context of classical gravitational scattering in four dimensions. More in detail, we show that the infinite impact parameter limit of the late-time gravitational field emitted during a classical scattering can be derived using these factorization theorems. The classical field obtained in this (infinite impact parameter) regime has an expansion in the frequency of the detector where the modes scale as ωn log ω with a vanishing memory.

Cylindrical gravitational waves in Einstein-Aether theory

Abstract Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $\Psi(r,t)$ and $H(r,t)$. However, in GR, $\Psi(r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13} \rightarrow 1$ and zero if $c_{13} \rightarrow -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA that might aid in the search for new physics in the cosmological background of stochastic gravitational waves discovered recently by the Pulsar Timing Array collaborations such as NANOGrav, EPTA, PPTA, InPTA, and CPTA.

Metric symmetry by design in general relativity

Abstract The usual derivation of Einstein’s field equations from the Einstein–Hilbert action is performed by silently assuming the metric tensor’s symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein’s attempted Unified Field Theory or Moffat’s Nonsymmetric Gravitational Theory. Explicitly enforcing the constraint by means of a Lagrange-multiplier term restores Einstein’s field equations, but the multiplier appears as an additional, unconstrained antisymmetric term. We briefly discuss the possible significance of this term with respect to a nonvanishing cosmological angular momentum, a sourced spin current, the nonsymmetric nature of the Einstein pseudotensor characterizing the energy–momentum of the gravitational field, and possible implications on attempts to obtain a quantum theory of gravity.

Геофизические исследования на разных этапах освоения месторождений медистых песчаников в Казахстане

Using the example of the Zhaman-Aybat deposit, the possibilities of geophysical methods at the stages of forecasting and solving prospecting and exploration geological problems of deposits of copper sandstones in Kazakhstan are shown. The position and dimensions of the Zhaman-Aybat structure and the depth of productive deposits are reliably determined by seismic exploration. According to the local positive anomalies of the gravitational field, separate blocks of rocks were identified, and according to the data of vertical dipole sounding, the depth of the high-resistance horizon identified with the roof of the rocks of the Zhezkazgan formation was determined. By probing the formation of the field in the depth range of 500- 800 m, local anomalies associated with productive deposits of the Taskuduk formation were traced. Geophysical studies of wells and the results of testing have increased the reliability of determining the parameters necessary for recalculation of copper ore reserves. Deep drilling has confirmed the high accuracy of geophysical work.

Inverting vertical gravity anomaly gradients using multidirectional data from a mean sea surface model: the case of the Arabian Sea

Advancements in satellite altimetry have significantly enhanced high-resolution mean sea surface (MSS) models, enabling the computation of high-resolution vertical gravity anomaly gradient (VGAG) models. This study focused on the methodology for computing VGAG models using MSS models, introducing innovative improvements to established techniques. Using the SDUST2020 MSS model within the Arabian Sea research area, the DTU22 and CNES-CLS22 mean dynamic topography (MDT) models, and the XGM2019e_2159 Earth gravity field model for the remove–restore process, the short-wavelength geoid was derived. To harness the extensive marine gravity field information within the MSS model, the study considered the complex marine environment and calculated the second-order derivatives of the geoid in multiple directions. These derivatives were then used to determine their north–south and east–west components through the least squares method, resulting in the computation of the short-wavelength VGAG. By restoring the long-wavelength VGAG, a VGAG model for the study area was established. Finally, the results were analyzed using the SIO V32.1 VGAG model (named curv). Experimental results demonstrated that this approach effectively extracted marine gravity field information from the MSS model using multidirectional data, mitigating the amplification of geoid uncertainties caused by second-order derivatives.Graphical

Gravitational waves derived from the elastic energy

The Adams‐Williamson equations adeptly characterize the pressure distribution within Earth's interior, highlighting the role of pressure in storing elastic energy. This stored energy forms the basis for deriving the Newtonian gravitational field. The variability of the dielectric constant and electric charge (alongside magnetic permeability and magnetic charge) in response to gravitational field strength renders Maxwell's equations applicable within the context of a strong gravitational field. Intriguingly, the wave equation satisfied by the gravitational field can be derived from Maxwell's equations.

Exploring the basic concepts of Calculus through a case study on motion in gravitational space

In universities, the Calculus course presents significant challenges year after year. In this article, we will demonstrate how to use methods of Realistic Mathematics Education (RME) to introduce the concepts of limits, differentiation, and integration based on high school kinematics and dynamics knowledge. All mathematical concepts are coherently built upon experiences, experiments, and fundamental dynamics knowledge related to motion in a gravitational field. With the help of worksheets created using GeoGebra or Microsoft Excel, students can conduct digital experiments and later independently visualize and relate abstract concepts to practical applications, thereby facilitating their understanding. Subject Classification: 97D40, 97I40, 97M50