Newtonian Gravity Research Articles

Cosmic voids and the kinetic analysis

The kinetic approach to the formation of the filaments in the large-scale matter distribution in the Universe is considered within the Vlasov formalism. The structures arise due to the self-consistent dynamics, along with the repulsive term in the modified Newtonian gravity which includes the cosmological constant. That modified gravity enables one to describe the Hubble tension as a result of two flows, the local and global ones. The criteria for formation of non–stationary semi-periodic structures in a system of gravitating particles described by Vlasov–Poisson equations are obtained in the case of that repulsive term. The obtained dispersion relations for the Vlasov equation in the vicinity of the singular point of the modified gravitational potential demonstrate the possibility of the emergence of filaments as coherent complex states of relative equilibrium in non–stationary systems as structures of low dimensions (walls), and voids between them, of scales (diameters) defined by the balance between the gravity and repulsive term of the cosmological constant.

Schrödinger–Poisson systems under gradient fields

A singularity-free generalisation of Newtonian gravity can be constructed (Lazar in Phys Rev D 102:096002, 2020) within the framework of gradient field theory. This procedure offers a straightforward regularisation of Newtonian gravity and remains equally well applicable to other fields, such as electromagnetic fields. Here, with the aim of finding potentially measurable effects of gradient fields on the dispersion properties of various media, we present a quantum kinetic treatment of matter under gradient fields. The method is based on the application of the Wigner–Moyal procedure to the modified Schrödinger–Poisson equation emerging in the framework of gradient field theory. This allows us to treat, on equal footing, three different scenarios, namely self-gravitating systems, plasmas, and cold atoms in magneto-optical traps. We address the signature of gradient fields in the elementary excitations of these media. In particular, we estimate this effect to be accessible in state-of-the-art plasma-based experiments. We discuss in detail the classical kinetic and hydrodynamic limits of our approach and obtain a class of generalised Lane–Emden equations, in the context of gradient field theory, which remain valid in the three scenarios discussed here.

Binary mergers in bootstrapped Newtonian gravity: Mass gap and black hole area law

We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the proper mass of Newtonian gravity and the proper mass of general relativity, which affects the interpretation of astrophysical and cosmological events. The aforementioned difference particularly provides important phenomenological constraints for the mass of the emitted matter and the compactness of the final object after the merger. The interpretation of the GW150914 signal in this theory also shows that LIGO's findings do not violate the mass gap, contrary to usual claims. We indeed find that typical stellar black hole masses can fit LIGO's data for a considerable range of compactness values. We calculate the black hole entropy in this context, which leads to a generalised black hole area law. Non-linear effects are found to effectively change only the gravitational strength via the renormalisation of Newton's constant in this case.

MICROSCOPE’s constraint on a short-range fifth force

The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical ‘free-falling’ test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE’s sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stiffness. By measuring the total stiffness of the forces acting on a test mass as it moves, and comparing it with the theoretical electrostatic stiffness (expected to dominate), it is a priori possible to infer constraints on the Yukawa potential parameters. However, we find that measurement uncertainties are dominated by the gold wires used to control the electric charge of the test masses, though their related stiffness is indeed smaller than the expected electrostatic stiffness. Moreover, we find a non-zero unaccounted for stiffness that depends on the instrument’s electric configuration, hinting at the presence of patch-field effects. Added to significant uncertainties on the electrostatic model, they only allow for poor constraints on the Yukawa potential. This is not surprising, as MICROSCOPE was not designed for this measurement, but this analysis is the first step to new experimental searches for non-Newtonian gravity in space.

On the Rotation Curve of Disk Galaxies in General Relativity

Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of general relativity (GR) instead of the effect of dark matter (DM) halos. In this paper, by using the well-known weak-field, low-velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles and compared with the predictions of Newtonian gravity for the same disks in absence of DM. As expected, the resulting rotation curves are indistinguishable, with GR corrections at all radii of the order v 2/c 2 ≈ 10−6. Next, the gravitomagnetic Jeans equations for two-integral stellar systems are derived, and then solved for the Miyamoto–Nagai disk model, showing that finite-thickness effects do not change the previous conclusions. Therefore, the observed phenomenology of galactic rotation curves at large radii requires DM in GR exactly as in Newtonian gravity, unless the cases here explored are reconsidered in the full GR framework with substantially different results (with the surprising consequence that the weak-field approximation of GR cannot be applied to the study of rotating systems in the weak-field regime). In this article, the mathematical framework is described in detail, so that the present study can be extended to other disk models, or to elliptical galaxies (where DM is also required in Newtonian gravity, but their rotational support can be much less than in disk galaxies).

Progress in the Composite View of the Newton Gravitational Constant and Its Link to the Planck Scale

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it was already pointed out in 1987 that this led to a circular problem; namely, that one must know G to find the Planck units, and that it is therefore of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is held by the physics’ community. However, we will claim that the circular problem was solved a few years ago. In addition, when one expresses the mass from the Compton wavelength formula, this leads to the conclusion that the three universal constants of G, h, and c now can be replaced with only lp and c to predict observable gravitational phenomena. While there have been several review papers on the Newton gravitational constant, for example, about how to measure it, we have not found a single review paper on the composite view of the gravitational constant. This paper will review the history of, as well as recent progress in, the composite view of the gravitational constant. This should hopefully be a useful supplement in the ongoing research for understanding and discussion of Newton’s gravitational constant.

(g−2)μ and screened modified gravity

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory.

The Restricted Six-Body Problem with Stable Equilibrium Points and a Rhomboidal Configuration

We explore the central configuration of the rhomboidal restricted six-body problem in Newtonian gravity, which has four primaries m i (where i = 1 , … 4 ) at the vertices of the rhombus a , 0 , − a , 0 , 0 , b , and 0 , − b , respectively, and a fifth mass m 0 is at the point of intersection of the diagonals of the rhombus, which is placed at the center of the coordinate system (i.e., at the origin 0,0 ). The primaries at the rhombus’s opposite vertices are assumed to be equal, that is, m 1 = m 2 = m and m 3 = m 4 = m ˜ . After writing equations of motion, we express m 0 , m , and m ˜ in terms of mass parameters a and b . Finally, we find the bounds on a and b for positive masses. In the second part of this article, we investigate the motion and different features of a test particle (sixth body m 5 ) with infinitesimal mass that moves under the gravitational effect of the five primaries in the rhomboidal configuration. All four cases have 16, 12, 20, and 12 equilibrium points, with case-I, case-II, and case-III having stable equilibrium points. A significant shift in the position and the number of equilibrium points was found in four cases with the variations of mass parameters a and b . The regions for the possible motion of test particles have been discovered. It has also been observed that as the Jacobian constant C increases, the permissible region of motion expands. We also have numerically verified the linear stability analysis for different cases, which shows the presence of stable equilibrium points.

Effects of photon field on entanglement generation in charged particles

The Bose-Marletto-Vedral (BMV) experiment [3, 4] is a proposal for testing the quantum nature of gravity with entanglement due to Newtonian gravity. This proposal has stimulated controversy on how the entanglement due to Newtonian gravity is related to the essence of quantum gravity and the existence of gravitons. Motivated by this, we analyze the entanglement generation between two charged particles coupled to a photon field. We assume that each particle is in a superposition of two trajectories and that the photon field is initially in a coherent state. Based on covariant quantum electrodynamics, the formula for the entanglement negativity of the charged particles is derived for the first time. Adopting simple analytic trajectories of the particles, we demonstrate the entanglement between them. It is observed that the entanglement is suppressed by the decoherence due to the vacuum fluctuations of the photon field. We also find that the effect of quantum superposition of bremsstrahlung appears in the entanglement negativity formula. The similar structures between the gravity theory and electromagnetic theory suggests that a similar feature may be observed in the entanglement generation by quantum gravitational radiation.

Approximating compact objects in bootstrapped Newtonian gravity: use of the canonical potential

We consider compact objects in a classical and non-relativistic generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory, which includes higher-order derivative interaction terms of the kind generically present in the strong-field regime of gravity. By means of a field redefinition, the original bootstrapped Newtonian action is written in a canonical Newtonian form with non-linear source terms. Exact analytic solutions remain unattainable, but we show that perturbative solutions of the canonical theory can be efficiently used to derive approximate descriptions of compact objects. In particular, using the canonical potential, we can more directly and generally show that the Arnowitt–Deser–Misner mass differs from the (Newtonian) proper mass due to the non-linear couplings in the theory. A few examples of sources with different density profiles are explicitly reanalysed in this framework.

Tidal deformability of crystallized white dwarfs in full general relativity

Space-based gravitational-wave detectors offer new prospects for probing the interior of white dwarfs in binary systems through the imprints of tidal effects on the gravitational-wave signal. Some of the binaries that will be observed could have evolved for long enough for the white dwarfs to be at least partially crystallized. The apsidal motion constant ${k}_{2}$ (also called the second gravitoelectric Love number) of a cold crystallized white dwarf is computed in full general relativity considering different compositions. The elasticity of the crystallized core is found to systematically reduce the tidal deformability, especially for low-mass stars. Fully relativistic results are compared to those obtained in Newtonian gravity. It is shown that the relativistic correction to the observable tidal deformability ${k}_{2}{R}^{5}$ (where $R$ is the stellar radius) is negligible for low-mass white dwarfs but becomes increasingly important for more massive white dwarfs. When approaching the maximum mass, the application of Newtonian theory instead of general relativity leads to dramatic errors. The case of eccentric binaries, for which the precession of the periastron causes a frequency splitting of the gravitational-wave signal depending on the apsidal motion constants of the two stars, is investigated. Future measurements of the precession rate by the Laser Interferometer Space Antenna, which is planned to be in operation within the next decade, could potentially provide estimates of the individual masses. It is found that the errors incurred by the neglect of the elasticity of the crystallized core could be very large, especially for low-mass white dwarfs. Gravitational-wave observations could thus provide a new way to study the crystallization of white dwarfs.

Passive directed dispersal of plants by animals

Conceptual gaps and imprecise terms and definitions may obscure the breadth of plant-animal dispersal relationships involved in directed dispersal. The term 'directed' indicates predictable delivery to favourable microsites. However, directed dispersal was initially considered uncommon in diffuse mutualisms (i.e. those involving many species), partly because plants rarely influence post-removal propagule fate without specialized adaptations. This rationale implies that donor plants play an active role in directed dispersal by manipulating vector behaviour after propagule removal. However, even in most classic examples of directed dispersal, participating plants do not influence animal behaviour after propagule removal. Instead, such plants may take advantage of vector attraction to favourable plant microsites, indicating a need to expand upon current interpretations of directed dispersal. We contend that directed dispersal can emerge whenever propagules are disproportionately delivered to favourable microsites as a result of predictably skewed vector behaviour. Thus, we propose distinguishing active and passive forms of directed dispersal. In active directed dispersal, the donor plant achieves disproportionate arrival to favourable microsites by influencing vector behaviour after propagule removal. By contrast, passive directed dispersal occurs when the donor plant takes advantage of vector behaviour to arrive at favourable microsites. Whereas predictable post-removal vector behaviour is dictated by characteristics of the donor plant in active directed dispersal, characteristics of the destination dictate predictable post-removal vector behaviour in passive directed dispersal. Importantly, this passive form of directed dispersal may emerge in more plant-animal dispersal relationships because specialized adaptations in donor plants that influence post-removal vector behaviour are not required. We explore the occurrence and consequences of passive directed dispersal using the unifying generalized gravity model of dispersal. This model successfully describes vectored dispersal by incorporating the influence of the environment (i.e. attractiveness of microsites) on vector movement. When applying gravity models to dispersal, the three components of Newton's gravity equation (i.e. gravitational force, object mass, and distance between centres of mass) become analogous to propagules moving towards a location based on characteristics of the donor plant, the destination, and relocation processes. The generalized gravity model predicts passive directed dispersal in plant-animal dispersal relationships when (i) animal vectors are predictably attracted to specific destinations, (ii) animal vectors disproportionately disperse propagules to those destinations, and (iii) those destinations are also favourable microsites for the dispersed plants. Our literature search produced evidence for these three conditions broadly, and we identified 13 distinct scenarios where passive directed dispersal likely occurs because vector behaviour is predictably skewed towards favourable microsites. We discuss the wide applicability of passive directed dispersal to plant-animal mutualisms and provide new insights into the vulnerability of those mutualisms to global change.

Development of Newton Gravity Student Worksheets on Problem-Based Learning Model to Improve Students' Scientific Argumentation Skills

The purpose of this study was to evaluate the validity, practicability, and efficiency of student worksheets for improving students' scientific argumentation skills on the topic of Newton's Law of Gravity. This study was conducted using the 4-D method, which consists of four stages of research: define, design, develop, and disseminate. It is restricted to the development stage in this study. The validity of the student worksheets was analysed based on aspects of content feasibility, guidelines, questions, scientific argumentation skills, and the Problem Based Learning model achieved an overall percentage of 93.75 %, 100 %, and 95.83 % respectively. 100 %, 100 %, 100 %. The practical aspect of student worksheets is analyzed based on the students' feedback in terms of the student worksheets component, Problem Based Learning model, enthusiasm, Newton's Law of Gravity topic, and scientific argumentation, with an average of 86 %, 82 %, 91.5 %, 88.5 %, and 88 % with robust criteria, respectively. The effectiveness of the student worksheets was determined using the outcomes of the scientific argumentation test's pretest and posttest, and they met the criteria for being very effective. The given test received an average n-gain score of 0.7342 in the interpretation category. Based on the research findings of the data analysis for validity, practicability, and effectiveness, it is possible to conclude that the student worksheets developed are feasible and effective in improving students' argumentation skills. Student worksheets based on a similar Problem Based Learning model could be designed to improve students' argumentation skills on other physics topics.

Contradiction in Einstein’s subjective explanation of the gravitational and kinematic time dilation

Einstein’s special and general relativity are relics from before quantum physics. If forces are transmitted by quanta, this must also apply to gravity. As light consist of quanta, it is only logical that gravitational quanta interact with light. In my article “Cognitive bias in physics with respect to Einstein’s relativity, demonstrated by the famous experiment of Pound and Rebka (1960), which in reality refutes Einstein’s general relativity” [R. G. Ziefle, Phys. Essays 35, 91 (2022)], I could demonstrate that Einstein’s “proper time” t 0 does not refer to reference frames but to gravitational potentials. That is why “Newtonian quantum gravity” [R. G. Ziefle, Phys. Essays 33, 99 (2020)] can predict the correct curvature of a light beam at the surface of the Sun. Also, the phenomena observed at the binary pulsar PSR B1913 + 16 can precisely be predicted by merely applying Kepler’s second law. If gravitational quanta move away from masses with the constant speed c of light, this coincides with Einstein’s postulate of a constant speed c of light with respect to reference frames, as a mass, such as a star or a planet, can also be defined as a reference frame. Therefore, Einstein’s found by chance an artificial and complicated method to calculate changes in space-time caused by motion, which are in reality additional gravitational effects caused by the relative velocity between gravitational quanta emitted by masses and other masses or photons.

How energy is conserved in Newtonian gravity

The concept underlying conservation of energy in a force field is that the work done by particles moving against the force represents energy removed from particles and added to energy in the field. For electromagnetic fields and charged particles, the transfer of energy between charges and local fields is described by Poynting's theorem. However, a similar local model for gravitational energy is not usually taught. In this paper, I derive the equations describing local conservation of energy in Newtonian gravity, discuss the well-known non-uniqueness of various terms, and show how comparison with Poynting's theorem provides insight into conditions for physical significance.

Towards a full general relativistic approach to galaxies

We analyse the dynamics of a single disk galaxy from a general relativistic viewpoint. We investigate dark matter (DM) effects in terms of a known family of stationary axially-symmetric solutions of Einstein equations coupled to a rotating dust. These effects are generated by the non-Newtonian features of such solutions and are ascribed to the essential role of frame dragging. Indeed, in such models, the off-diagonal elements of the metric are, in general, of the same order of magnitude of the diagonal ones. We generalize the results of Balasin and Grumiller (BG) to the physical case of differentially rotating dust. In particular, we find that for differential rotation the amount of energy density required to account for the flat rotation curves of disk galaxies is reduced with respect to the BG rigid rotation case. This stresses the discrepancy between Newtonian gravity and general relativity (GR), even at low velocities and low energy densities.

Cosmological Density Perturbation of Cold Dark Matter in Newtonian Gravity Scenario after Recombination: a Symmetry-Based Approach

Cosmological Density Perturbation of Cold Dark Matter in Newtonian Gravity Scenario after Recombination: a Symmetry-Based Approach

Crossover in Extended Newtonian Gravity Emerging from Thermodynamics

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the 1/r and 1/r2 forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics).

Seven nonstandard models coupling quantum matter and gravity

We review seven models which consistently couple quantum matter and (Newtonian) gravity in a nonstandard way. For each of them, we present the underlying motivations, the main equations, and, when available, a comparison with experimental data.

Stellar dynamics and dark matter in Local Group dwarf galaxies

When interpreted within the standard framework of Newtonian gravity and dynamics, the kinematics of stars and gas in dwarf galaxies reveals that most of these systems are completely dominated by their dark matter halos. These dwarf galaxies are thus among the best astrophysical laboratories to study the structure of dark halos and the nature of dark matter. We review the properties of the dwarf galaxies of the Local Group from the point of view of stellar dynamics. After describing the observed kinematics of their stellar components and providing an overview of the dynamical modelling techniques, we look into the dark matter content and distribution of these galaxies, as inferred from the combination of observed data and dynamical models. We also briefly touch upon the prospects of using nearby dwarf galaxies as targets for indirect detection of dark matter via annihilation or decay emission. This article reviews the properties of the dwarf galaxies of the Local Group from the point of view of their stellar dynamics and dark matter content and distribution, as inferred from the combination of observed data and dynamical models.