Newtonian Gravity Research Articles

Probing modified Newtonian dynamics with hypervelocity stars

We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. Hypervelocity stars are ejected from the Galactic center on radial trajectories with a null tangential velocity component in the reference frame of the Galaxy. They acquire tangential components due to the nonspherical components of the Galactic gravitational potential. Axisymmetric potentials only affect the latitudinal components, vθ, and non-null azimuthal components, vϕ, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, the azimuthal velocity components are proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is ∼750 km s−1 for 4 M⊙ stars and increases with decreasing HVS mass. We determine the upper limit of vϕ as a function of the galactocentric distance for these high-speed HVSs if MOND, in its quasi-linear formulation QUMOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of the azimuthal component, vϕ. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have vϕ values higher than the QUMOND upper limit if the dark matter halo is triaxial or if the dark matter halo and the baryonic components are axisymmetric but their two axes of symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs could in principle allow us to distinguish between the QUMOND scenario and the dark matter model. This test is currently limited by (i) the lack of a proper procedure to assess whether a star originates from the Galactic center and thus is indeed an HVS in the model one wishes to constrain; and (ii) the large uncertainties on the galactocentric azimuthal velocity components, which should be reduced by at least a factor of ∼10 to make this test conclusive. A proper procedure to assess the HVS nature of the observed stars and astrometric measurements with microarcsecond precision would make this test feasible.

The dynamics of three nearby E0 galaxies in refracted gravity

We tested whether refracted gravity, a theory of modified gravity that describes the dynamics of galaxies without the aid of dark matter, can model the dynamics of the three massive elliptical galaxies, NGC 1407, NGC 4486, and NGC 5846, out to ∼10Re, where the baryonic mass component fades out and dark matter is required in Newtonian gravity. We probed these outer regions with the kinematics of the globular clusters provided by the SLUGGS survey. Refracted gravity mimics dark matter with the gravitational permittivity, a monotonic function of the local mass density depending on three parameters,ϵ0,ρc, andQ, which are expected to be universal. Refracted gravity satisfactorily reproduces the velocity dispersion profiles of the stars and red and blue globular clusters, with stellar mass-to-light ratios in agreement with stellar population synthesis models, and orbital anisotropy parameters consistent with previous results obtained in Newtonian gravity with dark matter. The sets of the three parameters of the gravitational permittivity found for each galaxy are consistent with each other within ∼2σ. We compare the mean {ϵ0,Q,log10(ρc[g cm−3])} = {0.089−0.035+0.038, 0.47−0.21+0.29, −24.25−0.20+0.28} found here with the means of the parameters required to model the rotation curves and vertical velocity dispersion profiles of 30 disk galaxies from the DiskMass Survey (DMS):ρcandQagree within 1σwith the DMS values, whereasϵ0agrees within 3σ. This agreement suggests that ellipticals and disk galaxies allow for common values of the parameters of the permittivity and supports the universality of the permittivity function.

A Re-Interpretation of Quasi-Local Mass

Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.

Rayleigh’s stability criterion for circular orbits in Newtonian gravity and general relativity

O estudo de órbitas circulares sob a ação de forças centrais ou em espaços-tempos esfericamente simétricos é assunto bastante abordado em cursos introdutórios de mecânica clássica e de relatividade geral, respectivamente. A estabilidade dessas órbitas é comumente apresentada por meio da análise de máximos e mínimos do potencial efetivo para diversos valores distintos de momento angular. Apresentamos neste artigo, de forma didática, o critério de estabilidade de Rayleigh, que permite uma análise equivalente à do comportamento do potencial efetivo porém mais prática, levando em conta o comportamento de uma única função: o momento angular de órbitas circulares em função do raio. Argumentamos que esse critério, que geralmente não é apresentado nas disciplinas mencionadas acima, pode ser naturalmente incluído nas respectivas ementas, enriquecendo o aprendizado dos alunos.

On the Transition from Newtonian Gravity to General Relativity

On the Transition from Newtonian Gravity to General Relativity

The Phantom Dark Matter Halos of the Local Volume in the Context of Modified Newtonian Dynamics

Abstract We explore the predictions of Milgromian gravity (MOND) in the local universe by considering the distribution of the “phantom” dark matter (PDM) that would source the MOND gravitational field in Newtonian gravity, allowing an easy comparison with the dark matter framework. For this, we specifically deal with the quasi-linear version of MOND (QUMOND). We compute the “stellar-to-(phantom)halo mass relation” (SHMR), a monotonically increasing power law resembling the SHMR observationally deduced from spiral galaxy rotation curves in the Newtonian context. We show that the gas-to-(phantom)halo mass relation is flat. We generate a map of the Local Volume in QUMOND, highlighting the important influence of distant galaxy clusters, in particular Virgo. This allows us to explore the scatter of the SHMR and the average density of PDM around galaxies in the Local Volume, ΩPDM ≈ 0.1, below the average cold dark matter density in a ΛCDM universe. We provide a model of the Milky Way in its external field in the MOND context, which we compare to an observational estimate of the escape velocity curve. Finally, we highlight the peculiar features related to the external field effect in the form of negative PDM density zones in the outskirts of each galaxy, and test a new analytic formula for computing galaxy rotation curves in the presence of an external field in QUMOND. While we show that the negative PDM density zones would be difficult to detect dynamically, we quantify the weak-lensing signal they could produce for lenses at z ∼ 0.3.

Static and rotating white dwarf stars at finite temperatures

Static and rotating, cold and hot white dwarf stars are investigated both in Newtonian gravity and general theory of relativity, employing the well-established Chandrasekhar equation of state. The Hartle formalism is involved to construct and study uniformly rotating configurations of white dwarfs. The mass-radius, mass-central density, radius-central density and other basic relations of stable white dwarfs, consisting of pure helium and iron, are constructed for different temperatures at mass shedding limit. Stability of white dwarfs is analyzed with respect to the inverse beta decay process, pycnonuclear reactions and instabilities of general relativity. It is found that for a fixed mass hot white dwarfs consisting of pure iron are smaller in size, correspondingly denser with respect to the ones composed of light elements. In addition, it is shown that near the Chandrasekhar mass limit the mass of hot rotating white dwarfs is slightly less than for cold ones, though for low mass rotating white dwarfs and static ones in all mass range the situation is opposite.

The signature of the quadratic generalized uncertainty principle on the newtonian gravity and galaxy mass profile

In this study, we discuss the corrections implies by the presence of the general uncertainty principle (GUP) on Newton’s law of gravity by virtue of Verlinde’s proposal. We argue here that GUP leads to twofold modification, namely on the equipartition theorem and the holographic relation (Bekenstein-Hawking formula). Hence, following Verlinde’s proposal, we obtain quantum corrections term to the Newtonian gravity. In addition, we also report the quantum corrected mass profile of the galaxy. We restricted our derivation to first order in the GUP’s free parameter and compared it analytically with the other relevant works.

The Newtonian gravity of irregular shapes using STL files and 3D printing

The gravitational interactions of irregular shapes are rarely discussed in the compulsory schooling system and sometimes even ignored at the university level. This omission is due to the complexities encountered in extending Newton's law of gravitation to bodies that are not spherical. However, a deep understanding of the link between the gravity and the shape is quite important to interpret some basic facts of nature. In this paper, we show how simple concepts can be used to create a more general algorithm that has been implemented in matlab to compute the gravity of irregular bodies. Shapes are described in terms of Standard Tessellation Language files, the standard format for 3D printing. This approach to teaching allows students to model physical bodies, and the 3D representation of complex problems can help students acquire a more complete understanding of physics.

Relativistic Fractional-Dimension Gravity

This paper presents a relativistic version of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model recently introduced and based on the theory of fractional-dimension spaces. This extended version—Relativistic Fractional-Dimension Gravity (RFDG)—is based on other existing theories in the literature and might be useful for astrophysical and cosmological applications. In particular, in this work, we review the mathematical theory for spaces with non-integer dimensions and its connections with the non-relativistic NFDG. The Euler–Lagrange equations for scalar fields can also be extended to spaces with fractional dimensions, by adding an appropriate weight factor, and then can be used to generalize the Laplacian operator for rectangular, spherical, and cylindrical coordinates. In addition, the same weight factor can be added to the standard Hilbert action in order to obtain the field equations, following methods used for scalar-tensor models of gravity, multi-scale spacetimes, and fractional gravity theories. We then apply the field equations to standard cosmology and to the Friedmann-Lemaître-Robertson-Walker metric. Using a suitable weight vtt, depending on the synchronous time t and on a single time-dimension parameter αt, we extend the Friedmann equations to the RFDG case. This allows for the computation of the scale factor at for different values of the fractional time-dimension αt and the comparison with standard cosmology results. Future additional work on the subject, including studies of the cosmological late-time acceleration, type Ia supernovae data, and related dark energy theory will be needed to establish this model as a relativistic alternative theory of gravity.

Emergence of extended Newtonian gravity from thermodynamics

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale, whereas on the larger scale there emerges non-Newtonian gravity described by a nonlinear field equation containing a single coefficient. A comment is made on an estimation of the coefficient that has its origin in the thermodynamic property of the system.

Additional Solar System Gravitational Anomalies

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law F=G·M·mR2, except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, G^, which—across the six settings—varies with the mass of the smaller, moving body, m, so that G^=G×0.998+0.00016×lnm. While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

A large-scale heuristic modification of Newtonian gravity as an alternative approach to dark energy and dark matter

The peculiarities of the inverse square law of Newtonian gravity in standard big bang cosmology are discussed. It is shown that the incorporation of an additive term to Newtonian gravitation, as the inverse Yukawa-like field, allows removing the incompatibility between the flatness of the Universe and the density of matter in the Friedmann equation, provides a new approach for dark energy, and enables theoretical deduction of the Hubble–Lemaïtre law. The source of this inverse Yukawa-like field is the ordinary baryonic matter and represents the large-scale contribution of gravity in accordance with the Mach principle. It is heuristically built from a specular reflection of the Yukawa potential, in agreement with astronomical and laboratory observables, resulting null in the inner solar system, weakly attractive in ranges of interstellar distances, very attractive in distance ranges comparable to the clusters of galaxies, and repulsive in cosmic scales. Its implications in the missing mass of Zwicky, virial theorem, Kepler’s third law in globular clusters, rotation curves of galaxies, gravitational redshift, and Jean’s mass are discussed. The inclusion of the inverse Yukawa-like field in Newtonian gravitation predicts a graviton mass of at least 10−64 kg and could be an alternative to the paradigm of non-baryonic dark matter concomitant with the observables of the big bang.

External field effect in gravity

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory.

New test on the Einstein equivalence principle through the photon ring of black holes

Einstein equivalence principle (EEP), as one of the foundations of general relativity, is a fundamental test of gravity theories. In this paper, we propose a new method to test the EEP of electromagnetic interactions through observations of black hole photon rings, which naturally extends the scale of Newtonian and post-Newtoian gravity where the EEP violation through a variable fine structure constant has been well constrained to that of stronger gravity. We start from a general form of Lagrangian that violates EEP, where a specific EEP violation model could be regarded as one of the cases of this Lagrangian. Within the geometrical optical approximation, we find that the dispersion relation of photons is modified: for photons moving in circular orbit, the dispersion relation simplifies, and behaves such that photons with different linear polarizations perceive different gravitational potentials. This makes the size of black hole photon ring depend on polarization. Further assuming that the EEP violation is small, we derive an approximate analytic expression for spherical black holes showing that the change in size of the photon ring is proportional to the violation parameters. We also discuss several cases of this analytic expression for specific models. Finally, we explore the effects of black hole rotation and derive a modified proportionality relation between the change in size of photon ring and the violation parameters. The numerical and analytic results show that the influence of black hole rotation on the constraints of EEP violation is relatively weak for small magnitude of EEP violation and small rotation speed of black holes.

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems.

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.

Evolution of globular-cluster systems of ultra-diffuse galaxies due to dynamical friction in MOND gravity

Context. Dynamical friction can be used to distinguish Newtonian gravity and modified Newtonian dynamics (MOND) because it works differently in these frameworks. This concept, however, has yet to be explored very much with MOND. Previous simulations showed weaker dynamical friction during major mergers for MOND than for Newtonian gravity with dark matter. Analytic arguments suggest the opposite for minor mergers. In this work, we verify the analytic predictions for MOND by high-resolution N-body simulations of globular clusters (GCs) moving in isolated ultra-diffuse galaxies (UDGs). Aims. We test the MOND analog of the Chandrasekhar formula for the dynamical friction proposed by Sánchez-Salcedo on a single GC. We also explore whether MOND allows GC systems of isolated UDGs to survive without sinking into nuclear star clusters. Methods. The simulations are run using the adaptive-mesh-refinement code Phantom of Ramses. The mass resolution is 20 M⊙ and the spatial resolution 50 pc. The GCs are modeled as point masses. Results. Simulations including a single GC reveal that, as long as the apocenter of the GC is over about 0.5 effective radii, the Sánchez-Salcedo formula works excellently, with an effective Coulomb logarithm increasing with orbital circularity. Once the GC reaches the central kiloparsec, its sinking virtually stops, likely because of the core stalling mechanism. In simulations with multiple GCs, many of them sink toward the center, but the core stalling effect seems to prevent them from forming a nuclear star cluster. The GC system ends up with a lower velocity dispersion than the stars of the galaxy. By scaling the simulations, we extend these results to most UDG parameters, as long as these UDGs are not external-field dominated. We verify analytically that approximating the GCs by point masses has little effect if the GCs have the usual properties, but for massive GCs such as those observed in the NGC 1052-DF2 galaxy, further simulations with resolved GCs are desirable.

Larson\u2013Penston Self-similar Gravitational Collapse

Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state p=kvarrho , k>0, and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.

MOND-like behavior in the Dirac–Milne universe

Aims.Observational data show that the observed luminous matter is not sufficient to explain several features of the present universe, from gravitational structure formation to the rotational velocities in galaxies and clusters. The mainstream explanation is that the missing mass, although gravitationally active, interacts very weakly with ordinary matter. Competing explanations involve changing the laws of gravity at low accelerations, as in MOdified Newtonian Dynamics (MOND). Here, we suggest that the Dirac-Milne cosmology, a matter-antimatter symmetric cosmology where the two components repel each other, is capable of accounting for such an apparent modification of the Newtonian law, without invoking dark matter.Methods.Using a simple analytical approximation and 1D and 3D simulations, we study rotation curves and virial velocities and compare the mass observed in the simulations to the mass derived assuming Newtonian gravity. Using a modified version of theRAMSEScode, we study the Faber-Jackson scaling relation and the intensity of the additional gravitational field created by antimatter clouds.Results.We show that, in the Dirac-Milne universe, rotation curves are generically flat beyond a characteristic distance of ≈2.5 virial radii, and that the Tully-Fisher and Faber-Jackson scaling relations with an exponent ≈3 are satisfied. We show that the mass derived from the rotation curves assuming Newtonian gravity is systematically overestimated compared to the mass really present. In addition, the Dirac-Milne universe, featuring a polarization between its matter and antimatter components, presents a behavior similar to that of MOND, characterized by an additional surface gravity compared to the Newtonian case. We show that in the Dirac-Milne universe, at the present epoch, the intensity of the additional gravitational fieldgamdue to the presence of clouds of antimatter is on the order of a few 10−11m s−2, similar to the characteristic acceleration of MOND. We study the evolution of this additional accelerationgamand show that it depends on the redshift, and it is therefore not a fundamental constant.Conclusions.Combined with its known concordance properties on the SNIa luminosity distance, age, nucleosynthesis, and structure formation, the Dirac-Milne cosmology may then represent an interesting alternative to the standard cosmological model ΛCDM, MOND, and other scenarios for explaining the dark matter (or missing gravity) and dark energy conundrum.

Thick branes with inner structure in mimetic f(R) gravity

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in f(R) gravity. We obtain several typical thick brane solutions for f(R)=R+alpha R^2. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with df/dR>0 is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter alpha on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances.