Gravitational Energy Research Articles

Spooky Black Holes and Gravitomagnetism

Wide spread misconceptions about the reality of space curvature in General Relativity (GR) and their relevance in connection to the existence of black holes are revisited. The mean life of proposed black holes is estimated and their practical non existence is emphasized. The repulsive effect of gravitational self energy is underlined. The relevance of gravitomagnetism to account for alleged black hole effects is stressed.

The Milky Way atlas for linear filaments II. clump rotation versus filament orientation

Abstract Dense clumps distributed along filaments are the immediate medium for star formation. Kinematic properties of the clumps, such as velocity gradient and angular momentum, combined with filament orientation, provide important clues to the formation mechanism of filament-clump configurations and the role of filaments in star formation. By cross-matching the Milky Way atlas for linear filaments and the Structure, Excitation and Dynamics of the Inner Galactic Interstellar Medium (SEDIGISM) 13CO (2-1) data, we aim to derive the velocity gradient (${\cal {}G}$) and its direction ($\theta _{\cal {}G}$), the specific angular momentum (J/M), and the ratio (β) between the rotational energy and gravitational energy of clumps, as well as to investigate the alignment between clump rotation and filament orientation. We found a monotonic increase in J/M as a function of clump size (R), following a power-law relation J/M ∝ R1.5 ± 0.2. The ratio β ranges from 1.1 × 10−5 to 0.1, with a median value 1.0 × 10−3, suggesting that clump rotation provides insignificant support against gravitational collapse. The distribution of the angle between clump rotation ($\theta _{\cal {}G}$) and natal filament orientation is random, indicating that the clumps’ rotational axes have no discernible correlation with the orientation of their hosting filaments. Counting only the most massive clump in each filament also finds no alignment between clump rotation and filament orientation.

Do gravity data justify a rifted “Liguro-Provençal Basin”?

The geodynamic evolution of the Liguro-Provençal Basin and its crust and upper mantle structure remain debated, especially regarding the role of rifting in continental break-up and seafloor spreading. Our study incorporates updated datasets, including new gravity maps from the AlpArray Gravity Working Group (complete Bouguer, free air, and isostatic anomalies) for 3D modeling and gravity field analysis, seismic data from Lobster offshore campaigns for direct comparison, and geodynamic models, supplemented by seismic profiles from previous French and Italian campaigns to constrain the interpretation. We used GFZ’s IGMAS + software for interactive 3D modeling, creating a density model extending to 300 km depth that includes crustal and upper mantle inhomogeneities based on prior geodynamic models. This hybrid approach, with polygonal structures for the crust and voxels for the upper mantle, clarifies individual contributions to the gravity field. Extending initial gravity modeling from the SPP MB4D project INTEGRATE, our work provides a consistent 3D density model for the Alps and Ligurian Basin. The constrained 3D modeling and numerical analyses (terracing, clustering, filtering, curvature), along with vertical stress and gravitational potential energy calculations, suggest that rifting has significantly influenced the basin’s geological evolution.

Coal‐wall spalling prevention mechanism using advance‐grooving pressure relief in the large‐mining‐height working face of a shallow coal seam

AbstractIn mining, the roof structure of a working face with a large mining height in a shallow‐buried coal seam is prone to cutting instability in front of the support, which causes support crushing and coal‐wall spalling. This study analyzes 2201 working faces with large mining heights in the Haiwan No. 3 Mine by investigating the mechanical response law of coal walls under the transient excitation of roof structure instability. A mechanical model of coal walls under dynamic and static load coupling is established, revealing the formation mechanism of coal wall spalling and its main influencing factors. Prevention and control technologies of advanced grooving and pressure relief are proposed, and grooving parameters are determined. The results show that: During the mining process of large mining height working face in shallow buried coal seam, the step change of static response of coal wall is induced by the transient instability of roof structure, and the high abutment pressure is formed on the coal wall. At the same time, the strain energy and gravitational potential energy of roof cutting instability are released to form a dynamic load. Under the action of dynamic and static load, the plastic failure dissipation power of the coal wall is greater than the critical power, and the coal wall spalling occurs. The main influencing factors are mining load, mining height, and internal friction angle of the coal wall. The method of advanced grooving pressure relief can change the roof structure and coal force mechanism, by cutting off the connection between the coal wall and immediate roof, reducing the height of the coal wall force, effectively controlling the position of the roof cut off break line, reducing the static load effect of the roof on the coal, and transferring the position of the dynamic load response to the depth of the coal wall. When the grooving height‐depth ratio k is 0.75, the peak value of the abutment pressure moves 5.57 m to the front of the working face, and the pressure relief effect is the best. The above research results provide an effective active protection method for controlling coal wall spalling in fully mechanised working face with large mining height.

Development of stress field for the African tectonic plate from gravitational potential energy

Development of stress field for the African tectonic plate from gravitational potential energy

On the Mass of (Gravitational) Potential Energy

In classical mechanics, when a body freely moves or is externally forced to move in a conservative force field, such as a planet moving away from a star or a weight lifted from the floor, its kinetic energy or the work done on it is converted and stored as potential energy. The concept of potential energy was developed to uphold the fundamental principle of conservation of energy. According to the widely accepted interpretation of mass-energy equivalence, every form of energy has mass. This leads to the natural questions: does potential energy have mass? And if so, where is that mass located? We will start by briefly reviewing the issue through an examination of some key literature on the topic. The current consensus is that potential energy gets stored in the field energy of the interacting system. As a result of mass-energy equivalence, the equivalent mass is distributed throughout the entire space in some manner. However, this presents some difficulties. Here, like some other scholars in the past, we show that it contradicts the principles of special relativity and argue that potential energy does increase the mass of the bodies composing the system. We present an accessible thought experiment that heuristically corroborates that view specifically for the gravitational potential energy. We finally speculate on how that mass increase is distributed among the interacting bodies.

Mathematical model of molten iron and slag flow in the hearth

The stable hearth discharge is crucial for the operation of a blast furnace (BF). This study established a mathematical model for hearth discharge based on Bernoulli's principle, which considers the blast pressure, kinetic energy of molten iron and slag, gravitational potential energy, the pressure loss of molten iron and slag flowing through the deadman and taphole. It is found that the sharp increase of molten iron and slag flow is probably due to the fracture of the mud, while the sharp decrease of molten iron and slag flow is probably due to the blockage of the taphole by coke. This paper also studies the effect of operating parameters on the hearth discharge. With the increase of taphole plug time, the production rate and slag viscosity, the tap-end time will increase. With the increase of deadman voidage, the tap-end time will be shortened. The correctness of the mathematical model was verified by the actual flow rate of slag and molten iron.

Modified method of round Gaussian rings. Application to the two-planetary problem

A scheme of the modified method of round Gaussian rings, designed to study the secular evolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits may not coincide. The mutual gravitational energy of the rings 𝑊𝑚𝑢𝑡 is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function 𝑊𝑚𝑢𝑡, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to the equations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun-Jupiter-Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a function of time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.

Impact of the Source Material Gradation on the Disaster Mechanism of Underground Debris Flows in Mines

In mines where the natural caving method is used, the frequent occurrence of underground debris flows and the complex mine environments make it difficult to prevent and control underground debris flows. The source is one of the critical conditions for the formation of debris flows, and studying the impact of source material gradation on underground debris-flow disasters can effectively help prevent and control these occurrences. This paper describes a multiscale study of underground debris flows using physical model experiments and the discrete-element method (PFC3D) to understand the impact of the source material gradation on the disaster mechanism of underground debris flows from macroscopic and microscopic perspectives. Macroscopically, an increase in content of medium and large particles in the gradation will enhance the instantaneous destructive force. Large particles can more easily cause disasters than medium and fine particles with the same content, but the disaster-causing ability is minimized when the contents of medium and large particles exceed 50% and 60%, respectively. With increasing fine particle content, the long-distance disaster-causing ability and duration is increased. On the microscopic level, the source-level pairs affect the initial flow mode, concentration area of the force chain, average velocity, average runout distance, and change in energy of the underground debris flow. Among them, the proportion of large particles in the gradation significantly affects the change in kinetic energy, change in dissipative energy, time to reach the peak kinetic energy, and time of coincidence of dissipative energy and gravitational potential energy. The process of underground debris flow can be divided into a “sudden stage”, a “continuous impact stage”, and a “convergence and accumulation stage”. This work reveals the close relationship between source material gradation and the disaster mechanism of underground debris flows and highlights the necessity of considering the source material gradation in the prevention and control of underground debris flows. It can provide an important basic theory for the study of environmental and urban sustainable development.

A low-cost method for quantifying bouncing ball dynamics with smartphone video

Abstract This study employed a low-cost method for quantifying bouncing ball dynamics with smartphone video. High-speed video analysis was used to investigate the bouncing behaviour of different balls, including table tennis, rubber, and tennis balls, on a table tennis surface. To examine the effect of surface material on bouncing dynamics, the table tennis ball was also tested on wood and tile surfaces. Key parameters analysed included bounce height decay, the coefficient of restitution (COR), and the bounce half-life. Additionally, we measured the total bouncing time and analysed the relationship between changes in gravitational potential energy, kinetic energy, and total mechanical energy (ME). Our results revealed a significant correlation between the COR and the decay rate of bounce height. Balls with higher COR values, indicative of lower energy loss per bounce, exhibited slower decay rates, resulting in longer bounce half-lives and extended total bounce times. For instance, the table tennis ball on a tile surface demonstrated a high COR of 0.93, a bounce half-life of 4.65 bounces, and a total bounce time of 8.22 ± 0.34 s. This suggests that material properties such as stiffness and elasticity of both the ball and the surface significantly influence the COR and decay rate, beyond just surface smoothness. Furthermore, our analysis of ME changes in the bouncing balls aligns with theoretical predictions, providing insights into the energy transformations occurring during bouncing. This improved understanding can also be a valuable tool for educators, helping teachers and students bridge the gap between theory and real-world observations, leading to a deeper grasp of the concepts.

Inconsistency of modified gravity in cosmology

We show that there is a fundamental flaw in the application of modified gravity theories in cosmology, taking f(R) gravity as a paradigmatic example. This theory contains a scalar degree of freedom that couples to the matter stress-energy tensor but not to gravitational energy. However, when applied to cosmology this theory is unable to distinguish between gravitational and non-gravitational energy. Hence the cosmological version of the theory does not coincide with its own macroscopic average, and we show that this leads to order-one discrepancies. We argue that the same inconsistency is common to many other modified gravity theories with extra degrees of freedom. Our results put into question whether these theories can make sense as the cosmological average of a fundamental theory, hence challenging their physical significance.

From Newton's First Law to the Motion of Celestial Bodies

Newton's original work "Principles" was written in Latin. An English version translated two years after his death changed the first law from "in directum" to "in a right line." Later generations think that only static or uniform straight line motion is inertia, while excluding rotational motion. This article proposes that the gravitational potential energy of a planet's revolution is equal to its centrifugal kinetic energy (mυ2). The work done by an object is a process quantity, but kinetic energy is a state variable that can be divided into instantaneous kinetic energy and average kinetic energy. Uniform motion does not do work, and instantaneous kinetic energy in variable speed motion does not also do work, only the average kinetic energy of variable speed motion does work. Only the energy between work and the average kinetic energy of variable speed motion can be converted into each other. We have clarified the relationship between work and kinetic energy, completed the transition of the kinetic energy formula at low and high speeds, achieved the unification of the kinetic energy formula and the mass energy relationship formula, and explained the √2 factor in the escape velocity..

Numerical and theoretical modeling of water droplet impact on hydrophilic and superhydrophobic cones

The phenomenon of droplet impingement on solid surfaces is prevalent in various natural and industrial contexts. Research on impact dynamics on conical surfaces keeps emerging, with superhydrophobic cones receiving more attention than hydrophilic ones. This study systematically investigates water droplet impact dynamics on both hydrophilic and superhydrophobic cones using a two-phase numerical solver under different Weber numbers (We) and cone angles (φ). Three distinct phases are identified in the We–φ map to describe the different outcomes on each type of cones. Generally, deposition occurs ultimately on hydrophilic cones, whereas rebounding is observed on superhydrophobic ones. The maximum spreading area βAmax on hydrophilic cones depends only slightly on φ but consistently increases with We, following a scaling law of We0.5 at higher We. In contrast, on superhydrophobic cones, βAmax increases significantly with both We and φ, and the exponent in the scaling laws of βAmax with respect to We increases notably as φ increases. Three characteristic times are defined to describe important motion states on both types of cones. Corresponding scaling laws for each time with We are established. Two theoretical models are developed to predict the maximum spreading position for droplets on hydrophilic cones and the rebound position on superhydrophobic cones, respectively. Gravitational potential energy is included in the energy budget for both models, and an auxiliary viscous dissipation due to spontaneous spreading is accounted for the hydrophilic case. Satisfactory agreement between the theoretical and numerical results is achieved.

Crust and Mantle Flow From Central Tibetan Plateau to the Indo‐Burma Subduction Zone

AbstractThe extremely oblique Indo‐Burma subduction zone exhibits dextral strike‐slip faulting along the Sagaing, Kabaw, and Churachandpur‐Mao Faults as well as east‐west shortening between the Sagaing Fault and Bengal Basin. Through regional stress analysis, considering areas from central Tibet, around the eastern Himalaya Syntaxis, to Burma, it has been determined that the principal compressive stress directions align with the principal strain rates. The northeast‐southwest oriented compressive stress direction from the western Shan Plateau continues into Burma. Notably, P axes align with the topographic gradients, and T axes are sub‐parallel to the topographic contours in the Shan Plateau region south of 27°N. These stress patterns are consistent with a gravitational potential energy induced crustal and mantle flow. The alignment of the fast shear wave with the maximum strain rate and the colinear NW‐SE to E‐W fast direction of the SKS wave and T axis determined from focal mechanisms in the Shan Plateau suggest that the mantle lithosphere deforms in concert with the crust. We suggest crust and mantle flow south of the Red River Fault has resulted in widening of the lithosphere in the Shan Plateau in an east‐west direction. Therefore, the Sagaing Fault has bowed approximately 50–100 km westward if we assume that the Sagaing Fault was originally straight. Our results of regional stress inversion are consistent with late Miocene to present E‐W shortening in the Indo‐Burma subduction zone resulting from the release of gravitational potential energy from the central Tibetan Plateau.

Tracking the terminal velocity and energy of a parachutist: A video analysis for Physics classroom experiment

Abstract This study primarily focuses on tracking a parachutist’s terminal velocity and energy during a free fall using video analysis. Also, this study looks into related literature about the implications of this experiment for classroom practice. High-quality and slow-motion videos of free-falling slotted masses acting as parachutists were captured, and the terminal velocities and energies were analyzed through software tracker video analysis and modeling. The data from the software revealed that, indeed, the terminal velocity is directly proportional to the square root of the masses. The 200g parachutist reaches terminal velocity first, then the less massive parachutist. The generated kinetic energy, gravitational potential energy, and total mechanical energy graphs were similar to the literature. The tracker video analysis can indeed track a parachutist’s terminal velocity and energy. However, the acceleration due to gravitational needed to be measured correctly due to some errors in the experiment. Furthermore, the literature has cited positive and negative implications for classroom practice. This study can say that the positive outweighs the negative. The positive repercussions were about enhanced engagement, accuracy, and data precision, while the negative ones were about the school’s technological divide.

Giant Eruptions in Massive Stars and their Effect on the Stellar Structure

Giant eruptions (GEs) in luminous blue variables are years-to-decades-long episodes of enhanced mass loss from the outer layers of the star during which the star undergoes major changes in its physical and observed properties. We use the Modules for Experiments in Stellar Astrophysics stellar evolution code to model the evolution of a 70 M ⊙ star that undergoes a GE. We let the star evolve to the termination of the main sequence, and when it reaches T ≃ 19,400 K we emulate a GE by removing mass from its outer layers at a rate of 0.15 M ⊙ yr−1 for 20 yr. As mass is being lost, the star contracts and releases a substantial amount of gravitational energy. The star undergoes an initial ≃3 days of expansion followed by years of contraction. During that time the star tries to reach an equilibrium state, and as a result of loss in gravitational energy, its luminosity drops about 1 order of magnitude. As the GE terminates, we let the star continue to evolve without any further mass loss and track its recovery as it regains its equilibrium by adjusting its internal structure. After ≃87 yr it reaches a state very close to the one where the GE was first initiated. We suggest that at this point another GE or a cycle of GEs may occur.

On the Energy Budget of Starquake-induced Repeating Fast Radio Bursts

With a growing sample of fast radio bursts (FRBs), we investigate the energy budget of different power sources within the framework of magnetar starquake triggering mechanism. During a starquake, the energy can be released in any form through strain, magnetic, rotational, and gravitational energies. The strain energy can be converted from three other kinds of energy during starquakes. The following findings are revealed: (1) The crust can store free magnetic energy of ∼1046 erg by existing toroidal fields, sustaining 106 bursts with frequent starquakes occurring due to crustal instability. (2) The strain energy develops as a rigid object spins down, which can be released during a global starquake accompanied by a glitch. However, it takes a long time to accumulate enough strain energy via spindown. (3) The rotational energy of a magnetar with P ≲ 0.1 s can match the energy and luminosity budget of FRBs. (4) The budget of the total gravitational energy is high, but the mechanism and efficiency of converting this energy to radiation deserve further exploration.

Radiation Hydrodynamic Simulations of Massive Stars in Gas-rich Environments: Accretion of AGN Stars Suppressed by Thermal Feedback

Massive stars may form in or be captured into active galactic nuclei (AGN) disks. Recent 1D studies employing stellar-evolution codes have demonstrated the potential for rapid growth of such stars through accretion up to a few hundred solar masses. We perform 3D radiation hydrodynamic simulations of moderately massive stars’ envelopes in order to determine the rate and critical radius R crit of their accretion process in an isotropic gas-rich environment in the absence of luminosity-driven mass loss. We find that in the “fast-diffusion” regime where characteristic radiative diffusion speed c/τ is faster than the gas sound speed c s , the accretion rate is suppressed by feedback from gravitational and radiative advection energy flux, in addition to the stellar luminosity. Alternatively, in the “slow-diffusion” regime where c/τ < c s , due to adiabatic accretion, the stellar envelope expands quickly to become hydrostatic and further net accretion occurs on thermal timescales in the absence of self-gravity. When the radiation entropy of the medium is less than that of the star, however, this hydrostatic envelope can become more massive than the star itself. Within this subregime, the self-gravity of the envelope excites runaway growth. Applying our results to realistic environments, moderately massive stars (≲100M ⊙) embedded in AGN disks typically accrete in the fast-diffusion regime, leading to a reduction of steady-state accretion rate 1–2 orders of magnitudes lower than expected by previous 1D calculations and R crit smaller than the disk scale height, except in the opacity window at temperature T ∼ 2000 K. Accretion in slow diffusion regime occurs in regions with very high density ρ ≳ 10−9 g cm−3, and needs to be treated with caution in 1D long-term calculations.

Correlated scalar perturbations and gravitational waves from axion inflation

Abstract The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the gravitational energy density, Ω GW , at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of ζ and by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of 10-4 ÷ 10-2.

Instability and Evolution of Shocked Clouds Formed by Orthogonal Collisions between Magnetized Filamentary Molecular Clouds

Filamentary molecular clouds are recognized as primary sites for the formation of stars. Specifically, regions characterized by the overlapping point of multiple filaments, known as hub regions, are often associated with active star formation. However, the formation mechanism of this hub structure is not well understood. Therefore, to understand the formation mechanism and star formation in hub structures, as a first step, we investigate the orthogonal collisions between two filaments using three-dimensional ideal magnetohydrodynamical simulations. As a model of initial filaments, we use an infinitely long filament in magnetohydrostatic equilibrium under a global magnetic field running perpendicular to the filament axis. Two identical equilibrium filaments, sharing the same magnetic flux, are arranged with their long axes perpendicular to each other and given an initial velocity perpendicular to their long axes to replicate an orthogonal collision. We find three types of evolution after the shocked cloud is formed: collapse, stable, and expansion modes. The energy balance just after the filaments completely collide explains the future evolution of the shocked cloud. If the magnitude of gravitational energy is larger than the sum of the kinetic, thermal, and magnetic energies, the shocked cloud evolves in collapse mode. If the magnitude of gravitational energy is less than the sum of these energies, the cloud evolves in stable mode when the kinetic energy is relatively small and in expansion mode when the kinetic energy is sufficiently large.