二阶后牛顿光线方程

近来相继提出一系列的空间天体测量计划，要求考虑在多参考系中二阶后牛顿部分对光线传播的贡献，也就是说，必须讨论在最近完成的扩展的DSX体系下的二阶后牛顿(2PN)光线方程．DSX体系是在20世纪90年代初建立的，用来讨论对N个任意形状和组成、自转可变形物体的一套完整的一阶后牛顿(1PN)天体力学理论．在此建议采用迭代的方法来推导2PN光线方程．从度规和Christoffel记号出发推导太阳系中的2PN光线方程．当忽略掉更高阶的项时，2PN光线方程将回到在很多教科书中广泛出现的1PN光线方程．利用这套方程就可以计算太阳系的光线传播．     

Analytic black hole perturbation approach

In this talk, I review an analytic method for calculating gravitational radiation from a small mass particle orbiting a massive black hole. This method allows a systematic evalutation of the gravitational radiation to a very high order in post-Newtonian expansion, hence gives us useful information on the evolution of coalescing compact binary stars.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.     

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.     

On derivation of EIH (Einstein–Infeld–Hoffman) equations of motion from the linearized metric of general relativity theory

The half-century old idea of Infeld to use the variational principle of the general relativity field equations is reminded to show that the commonly employed EIH (Einstein–Infeld–Hoffman) equations of motion may be derived from the linearized (weak-field) metric alone. Based on it, the linearized metric might be sufficient for post-Newtonian celestial mechanics and astrometry enabling one to derive the post-Newtonian equations of motion and rotation of celestial bodies as well as the post-Newtonian equations of light propagation within the general relativity framework.     

双星系中两子星的自转对双星轨道变化的后牛顿效应

本文利用解摄动方程的平均值法求得在PPN框架中二体自转对轨道要素产生的后牛顿效应的长期变化影响．利用这一理论对CWCep和DRVul两颗双星中两子星的自转对轨道近星点和平近点角的长期摄动的后牛顿效应做了计算。结果表明：对于两个质量较大快速自转的子星,由此所产生的后牛顿效应的摄动量是不能忽视的。     

Post-Newtonian satellite orbits

The first post-Newtonian approximation of general relativity is used to account for the motion of solar system bodies and near-Earth objects which are slow moving and produce weak gravitational fields. The \(n\)-body relativistic equations of motion are given by the Einstein-Infeld-Hoffmann equations. For \(n=2\), we investigate the associated dynamics of two-body systems in the first post-Newtonian approximation. By direct integration of the associated planar equations of motion, we deduce a new expression that characterises the orbit of test particles in the first post-Newtonian regime generalising the well-known Binet equation for Newtonian mechanics. The expression so obtained does not appear to have been given in the literature and is consistent with classical orbiting theory in the Newtonian limit. Further, the accuracy of the post-Newtonian Binet equation is numerically verified by comparing secular variations of known expression with the full general relativistic orbit equation.     

White Dwarfs with Anisotropic Pressure in Postnewtonian Gravity

The theory of equilibrium of nonrotating, spherically symmetric neutron stars and white dwarfs is revisited. We propose that the condition for equilibrium is that the total energy is a minimum, for given baryon number, amongst configurations fulfilling Einstein's equations. The isotropy of the stress tensor is not assumed 'a priori'. Using this condition it is shown that, in post-Newtonian gravity, there are equilibrium configurations of white dwarfs, with local anisotropy, having mass above the Chandrasekhar limit. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cosmological Post-Newtonian Approximation in Flat Space-Time Theory of Gravitation

The 1-post-Newtonian approximation of perfect fluid in cosmological models of the theory of gravitation in flat space-time is studied. The equations of motion are given in evolution form. At high redshifts the terms of post-Newtonian approximation are important in studying the development of inhomogeneities on scales smaller than galaxies but at present time these terms only take effect on very large scales. This revised version was published online in July 2006 with corrections to the Cover Date.     

Parameterized post-Newtonian orbital effects in extrasolar planets

Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets.     

R-N场中雷达回波延迟实验的后后牛顿修正

从球对称引力场中光子在赤道面上的运动微分方程出发,采用后牛顿近似方法,讨论了Reissner-Nordstr(o|¨)m度规场中雷达回波延迟实验的后后牛顿修正.通过计算给出了后牛顿以及后后牛顿的修正结果,当荷电量Q为零时,该结果适用于电中性天体,其后牛顿部分的修正与经典文献一致.文中采用的近似展开方法同样适用于讨论更高阶的修正.雷达回波的高阶修正对目前展开的高精度空间引力试验有着重要的参考价值.     

Relativistic and the first sectorial harmonics corrections in the critical inclination

The problem of the critical inclination is treated in the Hamiltonian framework taking into consideration post-Newtonian corrections as well as the main correction term of sectorial harmonics for an earth-like planet. The Hamiltonian is expressed in terms of Delaunay canonical variables. A canonical transformation is applied to eliminate short period terms. A modified critical inclination is obtained due to relativistic and the first sectorial harmonics corrections.     

Astronomical relativistic reference systems with multipolar expansion: the global one

With the rapid development of techniques for astronomical observations,the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems.This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As a first step,the global solar system reference system is expressed as a multipolar expansion and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.     

Variant of the bimetric theory of gravitation. I. Parameterized post-newtonian formalism

A bimetric theory of gravitation with a Lagrangian that is quadratic with respect to “intensities” is considered. All the post-Newtonian parameters are determined and it is shown that they coincide with the respective parameters of the general theory of relativity. Translated from Astrofizika, Vol. 43, No. 2, pp. 303-312, April–June, 2000.     

Critical angular velocity of rigidly rotating white dwarfs

The equilibrium configurations of rigidly rotating white dwarfs are calculated numerically as an application of the finite difference — finite expansion method pioneered by Stoeckly. The latest version of the Harrison-Wheeler equation of state is used, together with the post-Newtonian equations of structure. No other approximation is made. The resulting critical values for the angular velocity agree in order of magnitude with a crude approximation to these values by Hartle and Thorne, but fractional differences in mean radius and in mass and eccentricities are very different.On leave from Department of Applied Mathematics, University of Cape Town, Cape Town.     

The Post-post-Newtonian Amendments of Radar Echo Delay Test in Reissner-Nordström Field

Starting from the differential equation of motion of photons on equatorial plane and in spherically symmetric field of gravitation and adopting the post-Newtonian approximate method, the post-post-Newtonian amendments of radar echo delay test in the Reissner-Nordström metric field are investigated. Via calculations the post-Newtionian and post-post-Newtonian amendments are obtained. When the electric charge Q is equal to zero, these results are applicable to electrically neutral celestial bodies, and the amendments of post-Newtonian parts are consistent with those provided by classical literature. The approximate expansion used in this paper can also be adopted to probe the amendments of still higher orders. The high-order amendments for radar echo have important significance to the ongoing high-precision spatial gravitation tests.     

Magnetohydrodynamic equilibrium conditions in the post-Newtonian approximation of general relativity

A set of equations, which are magnetohydrodynamic (MHD) equilibrium conditions in the post-Newtonian approximation of general relativity (PNA of GR), is obtained. The given system generalizes the previously obtained magnetohydrodynamic equilibrium conditions of classical mechanics and the hydrodynamic equilibrium conditions in the PNA of GR.     

Post-newtonian approximation of a nonstationary spherically symmetric star in flat space-time theory of gravitation

Starting from a previously studied theory of gravitation in flat space-time the post-Newtonian approximation of the gravitational field of an nonstationary spherically symmetric star is derived. To the post-Newtonian order the equations of motion and the conserved total energy of a collapsing star are given. Birkhoff's theorem holds to this accuracy.     

On the equilibrium figures of an ideal rotating fluid in the post-newtonian approximation of general relativity

A stability criterion is given for the equilibrium form of an ideal rotating fluid in the post-Newtonian approximation. This generalizes the known Lyapunov criterion in classical dynamics. The sphere stability is also investigated and it is shown that it is stable only whenR>22.2R _g (R is the relativistic sphere radius,R _g the Schwarzschild radius).