Yukawa Correction Research Articles

Unveiling the intricacies of attracting zones in magnetic binary systems: Investigating the impact of Yukawa correction

This study delves into the restricted three-body problem with a Yukawa correction to Newtonian gravitational forces, focusing on magnetic binary systems. We scrutinize the influence of Yukawa correction parameters (α, β) and the ratio of magnitude of magnetic moments (λ) on the system’s equilibrium points and their stability, zero-velocity curves. In our case, there exist of five and seven equilibrium points and all are found to be unstable for given range of parameters. Our examination extends to the basins of convergence and the existence of fractal under the influence of α and λ. Graphs drawn with the help of Wolfram Mathematica software vividly portray the parameter-driven evolution of equilibrium points, zero-velocity curves and basins of convergence. Furthermore, we explore the fractal characteristics within the basins of convergence, offering valuable insights into the complex dynamics of magnetic binary systems with Yukawa correction.

The Predictions of Noncollinear Equilibria Positions in ER3BP with Yukawa-Like Corrections

The existence and stability of noncollinear equilibrium points in the elliptic restricted three-body problem under the consideration of Yukawa correction to Newtonian potential are studied in this paper. The effects of various parameters (μ, ê, α, and λ) on the noncollinear equilibrium points are discussed briefly, and it is found that only ordinate of noncollinear equilibria E4,5 is affected by Yukawa correction while abscissa is affected by only mass parameter μ. The noncollinear equilibria was found linearly stable for a critical mass parameter μc. A critical point λ = ½ is also obtained for the critical mass parameter μc, and at this point, the critical mass parameter μc has maximum or minimum values according to α < 0 or α > 0, respectively.

Dynamics and Stability of the Two-Body Problem with Yukawa Correction to Newton’s Gravity, Revisited and Applied Numerically to the Solar System

In this manuscript, we review the motion of a two-body celestial system (planet–sun) for a Yukawa-type correction on Newton’s gravitational potential using Hamilton’s formulation. We reexamine the stability using the corresponding linearization Jacobian matrix, and verify that the conditions of Bertrand’s theorem are met for radii ≪1015 m, meaning that bound closed orbits are expected. Applied to the solar system, we present the equation of motion of the planet, then solve it both analytically and numerically. Making use of the analytical expression of the orbit, we estimate the Yukawa strength α and find it to be larger than the nominal value (10−8) adopted in previous studies, in that it is of order (α=10−4−10−5) for the terrestrial planets (Mercury, Venus, earth, Mars, and Pluto) and even larger (α=10−3) for the giant planets (Jupiter, Saturn, Uranus, and Neptune). Taking the inputs (rmin,vmas,e) observed by NASA, we analyse the orbits analytically and numerically for both the estimated and nominal values of α and determine the corresponding trajectories. For each obtained orbit, we recalculate the characterizing parameters (rmin,rmax,a,b,e) and compare their values according to the potential (Newton with/without Yukawa correction) and method (analytical and/or numerical) used. When compared to the observational data, we conclude that the path correction due to Yukawa correction is on the order of up to 80 million km (20 million km) as the maximum deviation occurring for Neptune (Pluto) for a nominal (estimated) value of α.

Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential

We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α ∈ − 1 , 1 is the coupling constant of Yukawa force to gravitational force, and λ ∈ 0 , ∞ is the range of Yukawa force. It is observed that as λ ⟶ ∞ , the mean-motion of the primaries n ⟶ 1 + α 1 / 2 and as λ ⟶ 0 , n ⟶ 1 . Further, it is observed that the mean-motion is unity, i.e., n = 1 for α = 0 , n > 1 if α > 0 and n < 1 when α < 0 . The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μ c = μ 0 + f α , λ , where μ 0 = 0.0385209 ⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μ c = μ 0 either for α = 0 or λ = 0.618034 , and the critical mass parameter μ c possesses maximum ( μ c max ) and minimum ( μ c min ) values in the intervals − 1 < α < 0 and 0 < α < 1 , respectively, for λ = 1 / 3 .

Nonsymmetric wormholes and localized big rip singularities in Einstein-Weyl gravity

The inclusion of the Weyl squared term in the gravitational action is one of the most simple, yet non trivial modifications to General Relativity at high energies. Nevertheless the study of the spherically-symmetric vacuum solutions of this theory has received much attention only in recent times. A new type of asymptotically flat wormhole which does not match symmetrically at a finite radius with another sheet of the spacetime is presented. The outer spacetime is characterized by a newtonian potential with a Yukawa correction, and has gravitational properties that can be arbitrarily close to the ones of a Schwarzschild black hole. The internal spacetime instead possesses a singularity at $r=\infty$ with the topology of a 2-dimensional sphere. The expansion scalar of geodesics reaching this singularity diverges in a finite amount of proper time, with a striking resemblance with the future singularity of the Big Rip cosmological scenario. In terms of the external Yukawa hair and mass $M$, these new wormholes fill a large region of the two-dimensional parameter space of physical solutions with $M>0$. On the contrary black holes, both of Schwarzschild and non-Schwarzschild nature, are confined on a line. We argue that this type of wormholes are ideal black hole mimickers.

Testing gravity with the Milky Way: Yukawa potential

We test a Yukawa correction to the Newtonian potential, making use of our own Galaxy - the Milky Way - as a testbed. We include as free parameter the Yukawa strength and range and the dark matter profile parameters, and compare several morphologies for the bulge, gas, and disk components, also using Bayesian model selection criteria. We employ up-to-date datasets for both the visible (baryonic) component of the Milky Way, and for the tracers of the gravitational potential (the Rotation Curve). We find that the data are consistent with the Newtonian potential, and constrain the Yukawa coupling $\beta$ to be negative and $\lambda$ to range along the curve $\lambda = a|\beta|^{c}$ with $a = (0.77 \pm 0.06)$ kpc and $c = -0.503\substack{+0.016 \\ -0.019}$.

Dynamics and stability of the two body problem with Yukawa correction

We explore the dynamics and stability of the two-body problem by modifying the Newtonian potential with the Yukawa potential. This model may be considered a theory of modified gravity; where the interaction is not simply the Kepler solution for large distance. We investigate stability by deriving the Jacobian of the linearized matrix equation and evaluating the eigenvalues of the various equilibrium points calculated during the analysis. The subcases of a purely Yukawa and purely Newtonian potential are also explored.

Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints

We consider higher-dimensional massive Brans-Dicke theory with Ricci-flat internal space. The background model is perturbed by a massive gravitating source which is pressureless in the external (our space) but has an arbitrary equation-of-state parameter $\mathrm{\ensuremath{\Omega}}$ in the internal space. We obtain the exact solution of the system of linearized equations for the perturbations of the metric coefficients and scalar field. For a massless scalar field, relying on the fine-tuning between the Brans-Dicke parameter $\ensuremath{\omega}$ and $\mathrm{\ensuremath{\Omega}}$, we demonstrate that (i) the model does not contradict gravitational tests relevant to the parameterized post-Newtonian parameter $\ensuremath{\gamma}$, and (ii) the scalar field is not ghost in the case of nonzero $|\mathrm{\ensuremath{\Omega}}|\ensuremath{\sim}O(1)$ along with the natural value $|\ensuremath{\omega}|\ensuremath{\sim}O(1)$. In the general case of a massive scalar field, the metric coefficients acquire the Yukawa correction terms, where the Yukawa mass scale $m$ is defined by the mass of the scalar field. For the natural value $\ensuremath{\omega}\ensuremath{\sim}O(1)$, the inverse-square-law experiments impose the following restriction on the lower bound of the mass: $m\ensuremath{\gtrsim}1{0}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{GeV}$. The experimental constraints on $\ensuremath{\gamma}$ require that $\mathrm{\ensuremath{\Omega}}$ be extremely close to $\ensuremath{-}1/2$.

Constraining Yukawa gravity from planetary motion in the solar system

In this work we used the observed additional perihelion precession in the Solar System, obtained from the observations of planets and spacecrafts, to study the possible existence of Yukawa correction term to the Newtonian gravitational potential. Our study was motivated by previous analyses which indicated the possible discrepancies from Newtonian gravity in this form and at wide range of astrophysical scales. Yukawa gravity was introduced to cure some shortcomings of General Relativity (GR) at galactic and extragalactic scales. We demonstrated that this form of gravity can give the values for orbital precession which are comparable or even in better agreement with observations than the corresponding predictions of GR. The obtained results can be used for setting stronger constraints on variation of the gravitational constant G, as well as on the fundamental constant δ of Yukawa gravity. Moreover, Yukawa gravity could be used to improve the results for the motion of planets, other Solar System bodies, as well as spacecrafts, and as a consequence, it can help us to get more reliable predictions for natural hazards in the Solar System, such as potential impacts by near-Earth objects.

The Poynting-Robertson effect in the Newtonian potential with a Yukawa correction

We consider a Yukawa-type gravitational potential combined with the Poynting-Robertson effect. Dust particles originating within the asteroid belt and moving on circular and elliptic trajectories are studied and expressions for the time rate of change of their orbital radii and semimajor axes, respectively, are obtained. These expressions are written in terms of basic particle parameters, namely their density and diameter. Then, they are applied to produce expressions for the time required by the dust particles to reach the orbit of Earth. For the Yukawa gravitational potential, dust particles of diameter $10^{ - 3}$ m in circular orbits require times of the order of $8.557 \times 10^{6}$ yr and for elliptic orbits of eccentricities $e =0.1, 0.5$ require times of $9.396 \times 10^{6}$ and $2.129 \times 10^{6}$ yr respectively to reach Earth’s orbit. Finally, various cases of the Yukawa potential are studied and the corresponding particle times to reach Earth’s are derived per case along with numerical results for circular and various elliptical orbits.

Yukawa effects on the mean motion of an orbiting body

In today’s gravity research there exist few modified gravitational theories which among other things predict the existence of a Yukawa-type correction to the classical gravitational potential. In this paper we study the Yukawa effect on the mean motion if any in a two-body scenario, assuming the influence of the existence of a possible Yukawa correction in the gravitational force of a primary. For that, we derive an equation in order to approximate the mean motion for secondary time rate of change of the orbiting body and its total variation over one revolution, under the influence of the non-Newtonian radial acceleration. Numerical results for Mercury and the companion star of the pulsar PSR $1913+16$ are calculated. For specific values of the parameters $\alpha$ and $\lambda$ , as given in the bibliography we have found that there is no corresponding Yukawa effect affecting the mean motion of the planet Mercury. On the other hand it appears that there is a periodic Yukawa effect that affects the mean motion of $\mbox{PSR}+16$ whose maximum numerical value occurs when the eccentric anomaly is equal to $180^{\circ}$ .

Testing long-distance modifications of gravity to 100 astronomical units

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of $10^{-7}$ times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

New upper limits on deviation from the inverse-square law of gravity in the solar system: a Yukawa parameterization

New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and λ is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun's quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α = 3.1 × 10−11 and λ = 0.15 au, and EPM2011 gives α = 5.2 × 10−11 and λ = 0.21 au. In both of them, α is at least 10 times less than the previous results.

Yukawa effects on the clock onboard a drag-free satellite

The Yukawa correction to the Newtonian gravitational force is accepted as a parameterization of deviations from the inverse-square law of gravity which might be caused by new physics beyond the standard model of particles and the general theory of relativity. We investigate these effects on the clock onboard a drag-free satellite: dynamics of the satellite and influence on the time transfer link. We find the Yukawa signal in the time transfer is much harder to detect with current state of clocks than those effects on the dynamics, especially the secular change of periastron, by laser ranging in the case of an artificial Earth satellite carrying a frequency standard with an orbit of $a=10^7$\,m and $e=0.01$.

Effects in the anomalistic period of celestial bodies due to a logarithmic correction to the Newtonian gravitational potential

We study the motion of a secondary celestial body under the influence of the logarithmic corrected gravitational force of a primary one. This kind of correction was introduced by Fabris and Campos (Gen. Relativ. Gravit. 41(1):93, 2009). We derive two equations to compute the rate of change of the anomalistic period with respect to the eccentric anomaly and its total variation over one revolution. In a kinematical sense, this influence produces an apsidal motion. We perform numerical estimations for some celestial bodies. We also compare our results to those obtained by considering a Yukawa correction.

Basic thermodynamic parameters of a black hole resulting from a Yukawa type of correction to the metric

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton’s “inverse-square law” of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the “universality of free fall” experiments. New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction λ≥1014 m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. In this paper we derive the basic thermodynamic parameters of such a Yukawa stationary spherically symmetric black hole. First, the expression for the event horizon of such a black hole is derived, with the help of which the temperature, entropy and heat capacity of this particular black hole are obtained. We have also obtained analytical expressions for the change of mass of such black hole, and also its corresponding evaporation time.

Calculation of radar signal delays in the vicinity of the Sun due to the contribution of a Yukawa correction term in the gravitational potential

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton’s “inverse-square law” of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the “universality of free fall” experiments. New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction λ≥1014 m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. To study the effect of the Yukawa correction to the gravitational potential and its corresponding signal delay in the vicinity of the Sun, we use a spherically symmetric modified space time metric where the Yukawa correction its added to the gravitational potential. Next, the Yukawa correction contribution to the signal delay is evaluated. In the case where the distance of closest approach is much less than the range λ, it results to a signal time delay that satisfies the relation t(b<λ)≅37.7t(b=λ).

COULOMB'S LAW CORRECTIONS FROM A GAUGE-KINETIC MIXING

We study the connection or equivalence between two well-known extensions of the Standard Model, that is, for the coupling between the familiar massless electromagnetism U (1) QED and a hidden-sector U (1)h, and axionic electrodynamics. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. When we compute in this way the static quantum potential for the coupling between the familiar massless electromagnetism U (1) QED and a hidden-sector U (1)h, the result of this calculation is a Yukawa correction to the usual static Coulomb potential. Previously,14, we have shown that axionic electrodynamics has a different structure which is reflected in a confining piece. Therefore, both extensions of the Standard Model are not equivalent. Interestingly, when the above calculation is done inside a superconducting box, the Coulombic piece disappears leading to a screening phase.

Aspects of Interacting Electromagnetic and Torsion Fields

The interaction energy is studied for the coupling of axial torsion fields with photons in the presence of an external electromagnetic field. To this end, we compute the static quantum potential. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done by considering a mass term for the gauge field, the Coulombic piece disappears leading to a screening phase.

On the1/cexpansion off(R)gravity

We derive for applications to isolated systems - on the scale of the Solar System - the first relativistic terms in the $1/c$ expansion of the space time metric $g_{\mu\nu}$ for metric $f(R)$ gravity theories, where $f$ is assumed to be analytic at $R=0$. For our purpose it suffices to take into account up to quadratic terms in the expansion of $f(R)$, thus we can approximate $f(R) = R + aR^2$ with a positive dimensional parameter $a$. In the non-relativistic limit, we get an additional Yukawa correction with coupling strength $G/3$ and Compton wave length $\sqrt{6a}$ to the Newtonian potential, which is a known result in the literature. As an application, we derive to the same order the correction to the geodetic precession of a gyroscope in a gravitational field and the precession of binary pulsars. The result of the Gravity Probe B experiment yields the limit $a \lesssim 5 \times 10^{11} \, \mathrm{m}^2$, whereas for the pulsar B in the PSR J0737-3039 system we get a bound which is about $10^4$ times larger. On the other hand the E\"ot-Wash experiment provides the best laboratory bound $a \lesssim 10^{-10} \, \mathrm{m}^2$. Although the former bounds from geodesic precession are much larger than the laboratory ones, they are still meaningful in the case some type of chameleon effect is present and thus the effective values could be different at different length scales.