Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to study the classical motion of a mass point in gravitational gauge field.First,by using Mathematica,a spherical symmetric solution of the field equation of gravitational gauge field is obtained,which is just the traditional Schwarzschild solution.Combining the principle of gauge covariance and Newton's second law of motion,the equation of motion of a mass point in gravitational field is deduced.Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field,we can discuss classical tests of gauge theory of gravity,including the deflection of light by the sun,the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun.It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.     

SPHERICALLY SYMMETRIC AND STATIC FIELDS IN LINEARIZED GAUGE THEORIES OF GRAVITATION

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational sourtion are obtained by maens of Green's function for the five Lagrangians with out ghosts and tachyons. In cases of four Lagrangians,the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-older, while in the case of the fifth hagrangian the space-time metric differs from the Schwarzschild one. Under both,Newtonian and-weak gravitational field approximations,the motion of a test particle without span should therefore be different from Newton's second law. As a result of the exchanged particles of spin o⁺ the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational "constant" G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant G_∞ is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).     

Black holes: a physical route to the Kerr metric

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole. In this paper I discuss the possibility of a quasi–stationary transition from rotating equilibrium configurations of normal matter to rotating bla ck holes.     

Gravitational lensing in the Kerr-Randers optical geometry

A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss–Bonnet theorem to a suitable osculating Riemannian manifold, adapted from a construction by Naz?m, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.     

THE CURRENTS AND SOME NEW RESULTS IN THE SKYRME MODEL

In this paper,we obtain the expressions of electromagnetic current,charged current,baryon current and neutral weak current in the Skyrme model by means of the gauge transformations.A relation available for both cases of m_π=0 and m_π≠0 is given.The mean square radius < r² >_A of axial form factor is calculated and the result shpws that its value is much smaller than the experimental datum.In addition,the expressions of < r² > _M,T=l and < r² >_M,T=0 in our derivations are different from those given in Ref.[4] by a factor 3/5.     

NULL GEODESIC EQUATION EQUIVALENT TO THE GEOMETRIC OPTICS EQUATION

In this paper, we proved that the null geodesic equations in general isotropic metric are rigorously equivalent to the differential equations bf light rays in a medium of flat 3-dimension.,31 space, which are the fundamental equations of geometrical optics, when the effect bf gravitational field tb light ray is taken as that of a variable "refractive index"。Our results provide the basic way to strictly describe the characteristics of some gravitational fields in terms of the Euclidean framework. It may be useful in the computation of modern astrometry and gravitational Lens effects. Finally, as a special example,the deflection of Iight by gravitational field is discussed by means of the formula of pure classical geometrical optics.     

关于引力场的能量问题

本文讨论引力场中局部区域的能量问题。这里提出了一个新的引力场总能量-动量赝张量密度,它所表示的引力场局部空间区域中的能量对纯空间坐标变换是不变量,因而引力场的局部区域能量具有确定的物理意义。关于Schwarzschild场的能量和动量,新的赝张量给出的结果要比现有广义相对论文献中的其他形式的赝张量所给出的结果较为合理。文中还讨论了在引力理论中质量与能量的关系问题。 关键词：     

双星系统的能量及其分布

本文援引胡宁所推广的引力场总能量动量赝张量密度式,计算了双星系统的能量,其结果是正常的。然而,这能量的分布却是不确定的;分布的规律基本上与孤立静止星球的席瓦兹外域场一致。如果认为场源物质所产生的引力场不再具有引力质量,则可决定该密度式中的n值,即引力场能量的分布也被确定。 关键词：     

Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge*

The exact metric of a Schwarzschild black hole in the true radiation gauge was recently reported.In this work, we base on this gravity and calculate the gravitational deflection of relativistic massive particles up to the fourth post-Minkowskian order. It is found that the result is consistent with the previous formulations for both the case of dropping the fourth-order contribution and the case of light deflection. Our result might be helpful for future high-accuracy observations.     

ON THE EXTERIOR SOLUTIONS OF A CHARGED MASS POINT IN GAUGE THEORIES OF GRAVITATION

In a case of spherically symtric and static field, exterior solutions of a charged mass point for the nine-parameter R+R² gravitational theories are investigated. We obtain results as follows: in the case of coupling constant (zP-2r+s)=0, solution without torsion is the Reissner-Nordstrom metric; otherwise there is no solution with vanishing torsion.     

Light’s bending angle due to black holes: from the photon sphere to infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray’s impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.     

计算光在引力场中偏折的新方法

利用光的量子论,能量守恒及弱等效原理得出电磁波传播在几何近似下,光线在引力场中的偏转角和波矢的关系. 利用引力场中电磁波方程,在弱场近似下给出了一般的计算光线偏转角度的方法. 具体计算了Schwarzchild引力场中光线的偏折及Kerr-Newman引力场中光线的偏折. 关键词： 引力场 电磁波方程 能量守恒 弱场近似     

MASSIVE SCALAR PARTICLE IN THE GRAVITATIONAL FIELD OF A MICROCOSMIC BLACK HOLE

The finite motion of a massive scalar particle in the gravitational field of a microcosmic black hole with weak relativistic approximation is discussed. In the Schwarzschild field, using the condition for balance σ=0, we obtain the relation between the produced and captured amplitudes for particles. In the Kerr field we show that the attenuation depends on the moment of the black hole and the attenuation process becomes an exciting one when ωh.     

Diagonal Metrics of Static, Spherically Symmetric Fields: The Geodesic Equations and the Mass-Energy Relation from the Coordinate Perspective

The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate time and an account of “gravitational acceleration from the coordinate perspective”. The results are applied to the Schwarzschild metric and to the so-called exponential metric. In an attempt to add an account of “gravitational force from the coordinate perspective”, the special relativistic mass-energy relation is generalized to diagonal metrics involving location dependent and possibly anisotropic light speeds. This move requires a distinction between two aspects of the mass of a test particle (parallel and perpendicular to the field). The obtained force expressions do not reveal “gravitational repulsion” for the Schwarzschild metric and for the exponential metric.     

Gravitational frequency-shift and deflection of light by quintessence

In this paper we investigate the gravitational frequency-shift and deflection of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analytical and numerical methods, we find that the gravitational frequency-shift of light in the Schwarzschild black hole space-time surrounded by the quintessence increases as the values of the normalization factor $c$ increases, but the gravitational frequency-shift of light decreases with the quintessential state parameter $ \omega_{\rm q}$ increasing. We also calculate the deflection of light by quintessence and find that the deflection rate decreases as the values of the quintessential parameters $c$ and $ \omega_{\rm q}$ increase.     

Test on Application Range of QCD Sum Rules from Baryon Spectroscopy

By considering the nonperturbative QCD effect via quark and gluon condensates, the confinement terms in effective q-q potential can automatically be given. A potential in the form of (-2α,/3r) + Σ_n^∞ a_2n+1r²ⁿ⁺¹ + (Yukawa-type terms) where positive and negative signs appear alternatively in a_2n+1's is proposed. To testify the validity range of QCD sum rules, the experimental baryon spectrum is fitted and the values of azn+l's as well as their signs are obtained. It is found that in the baryon spectrum calculation, the terms of r³ snd r⁵ are important and higher terms beyond r⁵ can be neglected. Comparing these values with the result calculated from QCD sum rules, some agreements and disagreements are found.     

Metric gravitation with a two parameter family of static spherically symmetric space-times

Among the variety of all conceivable metric theories of gravitation, Lorentz curvature dynamics is the most geometric extension of Einstein's field equations to fit the solar system data. In this framework two parameters determine the asymptotic form of a static spherically symmetric space-time (without imposing Einstein's conditions); these two parameters are the active gravitational mass of the source and the PPN parameter γ. The Lorentz connection is shown to satisfy covariant evolution equations which preserve either of these two parameters; furthermore, right and left oriented space-times differ in their Lorentz connection. Deviations from the Schwarzschild character find an interpretation in terms of a new object, the Lorentz curvature energy-momentum tensor, which always vanishes identically under the restriction of Einstein's conditions. These deviations contribute strongly to the gravitational force only in the neighbourhood of the Schwarzschild sphere.     

Scattering of particles by deformed non-rotating black holes

We study the excitation of axial quasi-normal modes of deformed non-rotating black holes by test particles and we compare the associated gravitational wave signal with that expected in general relativity from a Schwarzschild black hole. Deviations from standard predictions are quantified by an effective deformation parameter, which takes into account deviations from both the Schwarzschild metric and the Einstein equations. We show that, at least in the case of non-rotating black holes, it is possible to test the metric around the compact object, in the sense that the measurement of the gravitational wave spectrum can constrain possible deviations from the Schwarzschild solution.