We performed various tests on a cosmological model in which the string gauge field, and its coupling to matter, is used to explain the rotation dynamics of stars in a galaxy. Observations used include perihelion precession and galaxy rotation curves. We solved precession motions for perturbations of 1) a Lorenz-like force and 2) a general power law central force. For the latter case, a simple rule judging pro/retrograde motions is derived. We attributed the precession of solar system planets to the force due to the string field and calculated the field strengths. We then fitted the resultant field strengths with a profile consisting one part generated by the Sun and another background due to other matter in the Milky Way. We used the Milky Way rotation curve to estimate the field strength and compared it with the one found by precession. The field strengths in another 22 galaxies are also analyzed. The strengths form a range that spans 2 orders of magnitude and contains the value found for the Milky Way. We also deduced from the model a relation between field strength, galaxy size and luminosity and verified it with data of the 22 galaxies.
It is now known that, apart from black holes, some naked singularities can also cast shadows which provide their possible observable signatures. We examine the relevant question here as to how to distinguish then these entities from each other, in terms of further physical signatures. We point out that black holes always admit timelike bound orbits having positive perihelion precession. Also, while a naked singularity with a photon sphere can cast a shadow, it could also admit positive perihelion precession for such orbits, thereby mimicking a black hole. This indicates that compact objects wi…
Killing symmetries are revisited in $d$$=$$5$ bulk geometric torsion (GT) perturbation theory to investigate the perihelion precession. Computation reveals a non-perturbative (NP) modification to the precession known in General Relativity (GR). Remarkably the analysis re-assures our proposed holographic correspondence between a perturbative GT in bulk and a boundary GR coupled to $B_{2}$$ \wedge $$F_{2}$. In fact the topological correction is sourced by a non-Newtonian potential in GR and we identify it with an ``electro-gravito'' dipole. Interestingly the dipole correction is shown to possess…
The equivalence principle is important in fundamental physics. The fifth force, as a describing formalism of the equivalence principle, may indicate the property of an unknown theory. Dark matter is one of the most mysterious objects in the current natural science. It is interesting to constrain the fifth force of dark matter. We propose a new method to use perihelion precession of planets to constrain the long-range fifth force of dark matter. Due to the high accuracy of perihelion precession observation, and the large difference of matter composition between the Sun and planets, we get one o…
Higher order corrections (up to n-th order) are obtained for the perihelion precession in binary systems like OJ287 using the Schwarzschild metric and complex integration. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $r_s/\left(a(1-e^2)\right)$.}The results are compared with other expansions that appear in the literature giving corrections to second and third order. Finally, we simulate the shape of relativistic orbits for binary systems with different masses.
Higher order corrections are obtained for the perihelion precession in binary systems like OJ287, Sagittarius A*-S2 and H1821+643 using both the Schwarzschild metric and the Kerr metric to take into account the spin effect. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $ε\equiv r_s/\left(a(1-e^2)\right)$ and $ε^{*} \equiv \left(1- \frac{2 αE'}{cJ}\right) ε$.The results are compared with those obtained in a previous paper.
In this paper, the perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the main equation is obtained. As the application of this main equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution in $f(R)$ gravity have been taken for the examples. We find that both the electric charge and $f(R)$ gravity can affect the perihelion precession and deflection of light, while the cosmological constant can only effect the perihelion precession. Moreover, we clarify a subtlety in the deflection of light in t…
We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim \& Kazanas (1989). To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant $Λ$. We show that besides the general relativistic terms obtained earlier from the Schwarzschild - de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the lin…
We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to comp…
In the framework of the emergent gravity scenario by Verlinde, it was recently observed by Liu and Prokopec that, among other things, an anomalous pericenter precession would affect the orbital motion of a test particle orbiting an isolated central body. Here, it is shown that, if it were real, its expected magnitude for the inner planets of the Solar System would be at the same level of the present-day accuracy in constraining any possible deviations from their standard perihelion precessions as inferred from long data records spanning about the last century. The most favorable situation for …
We study the equations of motion of the massive and massless particles in the Schwarzschild geometry of general relativity by using the Laplace-Adomian Decomposition Method, which proved to be extremely successful in obtaining series solutions to a wide range of strongly nonlinear differential and integral equations. After introducing a general formalism for the derivation of the equations of motion in arbitrary spherically symmetric static geometries, and of the general mathematical formalism of the Laplace-Adomian Decomposition Method, we obtain the series solution of the geodesics equation …
The standard model particles can be gauged in an anomaly free way by three possible gauge symmetries namely ${L_e-L_μ}$, ${L_e-L_τ}$, and ${L_μ-L_τ}$. Of these, ${L_e-L_μ}$ and ${L_e-L_τ}$ forces can mediate between the Sun and the planets and change the perihelion precession of planetary orbits. It is well known that a deviation from the $1/r^2$ Newtonian force can give rise to a perihelion advancement in the planetary orbit, for instance, as in the well known case of Einstein's gravity which was tested from the observation of the perihelion advancement of the Mercury. We consider the long ra…
C. M. Will in a recent Letter [arXiv:1802.05304] predicts a new Mercury's precession rate which is $100$ times larger than the second-post-Newtonian contribution, our calculation is about $30$ times larger. Thus the new Mercury's precession rate is about $6.4\ast 10^{-8}$, instead of $6.2\ast 10^{-8}$, degrees per century.
Secular increase of the Astronomical Unit and perihelion precessions as tests of the Dvali-Gabadadze-Porrati multi-dimensional braneworld scenario
最近，三个不同的研究小组（Krasinsky和Brumberg，Pitjeva，Standish）报告了天文单位（太阳系的长度尺度）的意外长期增长。喷气推进实验室最新的测量值为7+-2 m cy^-1。目前，无论是在经典物理学领域，还是在爱因斯坦广义相对论通常的四维框架中，都没有能够容纳这种观察到的现象的解释。Dvali-Gabadadze-Porrati膜世界方案是一个多维引力模型，旨在解释在没有暗能量的情况下观测到的宇宙加速现象。除此之外，Dvali-Gabadadze-Porrati膜世界方案还预测了近日点的长期位移，这是由Lue和Starkman提出的，对于太阳系的所有行星来说，该位移为5 10^-4 arcsec cy^-1。它得出地日距离的变化约为6 m cy^-1，这与天文单位的观测速率在1 σ水平上是一致的。最近测量的太阳系内行星近日点长期运动的修正，在1-sigma水平上与水星和火星的Lue-Starkman效应的预测值一致，在2-sigma水平上与地球的Lue-Starkman效应的预测值一致。
In this work we explore some mathematical physics aspects of the spherically symmetric Lovelock black hole in high dimensions. Intended for this aim, we thoroughly consider the metric corresponding to the five-dimensional Lovelock black hole spacetime. We construct the strong retractions by the geodesic equations on the background under consideration. As a result, from the topological point of view, we construct the theory of strong homotopy retract, which will allow us, in principle, to better understand some of its suitable applications on astrophysics and cosmology, in particular, in the an…
The Hermean average perihelion rate $\dotω^\mathrm{2PN}$, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from $-18$ to $-4$ microarcseconds per century $\left(μ\mathrm{as\,cty}^{-1}\right)$, depending on the true anomaly at epoch $f_0$. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun's gravitational field. An evaluation of the merely formal un…
We derive here the orbit equations of particles in naked singularity spacetimes, namely the Bertrand (BST) and Janis-Newman-Winicour (JNW) geometries, and for the Schwarzschild black hole. We plot the orbit equations and find the Perihelion precession of the orbits of particles in the BST and JNW spacetimes and compare these with the Schwarzschild black hole spacetime. We find and discuss different distinguishing properties in the effective potentials and orbits of particle in BST, JNW and Schwarzschild spacetimes, and the particle trajectories are shown for the matching of BST with an externa…
The perihelion precession, the deflection of light, and the radar echo delay are classical tests of General Relativity here used to probe brane world topologically charged black holes in a f(R) bulk and to constrain the parameter that arises from the Shiromizu-Maeda-Sasaki procedure applied to a f(R) bulk as well. The existing Solar system observational data constrain the possible values of the tidal charge parameter and the effective cosmological constant including f(R) brane world effects. We show that the observational/experimental data for both perihelion precession and radar echo delay ma…
We make use of the absence of Lense-Thirring precession of the innermost megamaser clumps around black holes in order to place upper limits on the spin amplitude of seven black holes at the center of megamaser galaxies: NGC 4258, NGC 2273, UGC 3789, NGC 3393, NGC 5495, NGC 5765b, and UGC 6093. The constraints are derived by requiring that the associated precession time-scale be longer than the age of the megamaser clumps, in order to preserve the single-plane geometry of the megamasers.
Solar System motions and the cosmological constant: a new approach
我们利用一些行星近日点的牛顿-爱因斯坦长期岁差的修正（水星，地球，火星，木星，土星），俄罗斯天文学家E. V. Pitjeva在全球范围内将近一个世纪的数据与EPM 2004星历表相匹配，为了检验在Schwarzschild-de Sitter（或Kottler）时空框架中由均匀宇宙学常数λ引起的近日点进动的表达式。我们比较这样一个额外的速率估计修正的行星近日点岁差，采取他们的比率为不同的行星对，而不是使用一个近日点在一个时间为每个行星分别，到目前为止，在文献中。答案是完全否定的，即使进一步将皮特杰瓦公布的近日点额外岁差估计的误差重新缩放10倍（土星甚至100倍）。我们的结论也适用于任何其他的度规扰动具有相同的依赖于空间坐标，因为那些引起的其他广义相对论宇宙学的情况下，许多修改后的引力模型。目前正在进行的和计划中的行星际航天器飞行任务应能提高我们对行星轨道的认识，允许更严格的限制。
Can the Pioneer anomaly be induced by velocity-dependent forces? Tests in the outer regions of solar system with planetary dynamics
本文分析了最近提出的一些速度相关力对太阳系外行星（从木星到冥王星）轨道运动的影响，并将他们的预测（近日点\varpi或半长轴a的经度和偏心率e的长期变化）与E. V. Pitjeva使用EPM 2006星历表进行的最新观测测定相比较。事实证明，虽然预测的a百年位移是如此之大，以至于除了海王星之外，所有行星都可以很容易地检测到，但预测的\varpi异常岁差太小了，除了木星之外，所以它们仍然与标准牛顿-爱因斯坦近日点岁差的估计修正相一致。因此，我们倾向于放弃那些预测a和e长期变化的额外力，也是出于其他一些原因，而给那些预测仍然无法检测到近日点岁差的模型一个机会，至少在观测上是这样。当然，必须为它们找到充分的理论基础。
Preliminary bounds of the gravitational Local Position Invariance from Solar System planetary precessions
在参数化后牛顿（PPN）形式的框架下，我们计算了长期的首选位置（PL）的影响，与Whitehead参数$ξ$，除了半长轴$a$本地化的两体系统的所有开普勒轨道要素成比例。它们违反了由广义相对论（GR）实现的引力局部位置不变性（LPI）。利用太阳系行星历表领域的最新研究成果，得到了$ξ$的初步界。没有探测到火星的任何异常近日点岁差，使我们能够间接地推断出$|ξ|\leq 5.8\times 10^{-6}$。\textcolor{black}{Such a bound is close to the constraint, of the order of $10^{-6}$, expected from the future BepiColombo mission to Mercury. As a complementary approach, the PL effects should be explicitly included in the dynamical models fitted to planetary data sets to estimate $ξ$ in a least-square fashion in a dedicated ephemerides orbit solution.}在$<3σ$水平上用EPM2011星历表确定的金星和木星异常近日点岁差的比率，…
In this paper, we investigate the anomalous planets precession in the nearly-newtonian gravitational regime. This limit is obtained from the application of the slow motion condition to the geodesic equations without altering the geodesic deviation equations. Using a non-standard expression for the perihelion advance from the Weyl conformastatic vacuum solution as a model, we can describe the anomaly in planets precession compared with different observational data from Ephemerides of the Planets and the Moon (EPM2008 and EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using …
Advances in the measurement of the Lense-Thirring effect with planetary motions in the field of the Sun
E. V. Pitjeva通过使用EPM 2006星历表的动力学模型处理超过400，000个不同类型的行星观测数据，最近估计了对牛顿-爱因斯坦金星近日点进动的修正为每世纪-0.0004 +/- 0.0001弧秒。根据广义相对论的预测，金星近日点的Lense-Thirring岁差为每世纪-0.0003角秒。事实证明，无论是其他错误建模/未建模的标准牛顿/爱因斯坦效应，还是外来效应，假设，例如，解释先锋异常，可能导致了确定的额外岁差的金星轨道，因此，可以合理地归因于太阳的重力磁场，而不是在EPM 2006星历的例程建模。然而，必须指出的是，引用的错误是正式的，统计的一个;现实的不确定性可能更大。未来对内行星星历表的改进，包括信使号和金星快车号的跟踪数据，应该会进一步提高这种广义相对论测试的准确性和一致性，这也将有利于其他天文学家团队对近日点（和节点）的额外岁差的独立估计。
We launch a first investigation into how a light scalar field coupled both conformally and disformally to matter influences the evolution of spinning point-like bodies. Working directly at the level of the equations of motion, we derive novel spin-orbit and spin-spin effects accurate to leading order in a nonrelativistic and weak-field expansion. Crucially, unlike the spin-independent effects induced by the disformal coupling, which have been shown to vanish in circular binaries due to rotational symmetry, the spin-dependent effects we study here persist even in the limit of zero eccentricity,…
Mercury and frame-dragging in light of the MESSENGER flybys: conflict with general relativity, poor knowledge of the physical properties of the Sun, data reduction artifact, or still insufficient observations?
广义相对论利用日震学中太阳的角动量S = 190 x 10^39 kg m^2 s^-1，预测水星近日点经度的兰斯-瑟林岁差为-2.0毫角秒/世纪（在天体赤道参考系中计算）。在4-σ水平上，它与标准牛顿/爱因斯坦岁差的0.4 +/- 0.6毫角秒/世纪修正值不一致，只要后者完全归因于标架拖曳。补充岁差是最近用INPOP 10a星历表与一个长行星数据记录（1914-2010年）进行全球拟合确定的，其中包括2008-2009年从信使号航天器收集的3个数据点。INPOP 10a模型根本不包括太阳重力磁场，因此它的特征可能在数据简化过程中被部分删除。另一方面，Lense-Thirring进动可能在一定程度上被竞争进动所抵消，这些竞争进动是由太阳四极质量矩和PPN参数β进入Schwarzschild类1 PN进动的小错误建模引起的，两者都是在INPOP 10a中建模的。相反，水星本身的扁率对其近日点的影响可以忽略不计。最大的单个小行星和小行星环的错误模型行为也是如此。未来对目前正在进行的信使号任务的更多观测结果的分析将进一步阐明这一问题，如果得到证实，可能会挑战我们目前对目前公认的引力定律和/或太阳物理特性的看法。
The predicted Lense-Thirring perihelion precession of Mercury induced by the Sun's angular momentum through its general relativistic gravitomagnetic field amounts to 2 milliarcseconds per century. It turned out to be compatible with the latest experimental determinations of the supplementary perihelion precession of Mercury with the INPOP15a ephemerides, whose accuracy level has nowadays reached the magnitude of the predicted relativistic effect itself thanks to the analysis of some years of tracking data of the MESSENGER spacecraft, which orbited Mercury from 2011 to 2015. A dedicated analysi…
