Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation

In this paper we explore how far the post-Newtonian theory, [9] goes in overcoming the difficulties associated with anisotropic homogeneous cosmologies in the Newtonian approximation. It will be shown that, unlike in the Newtonian case, the cosmological equations of the post-Newtonian approximation are much more in the spirit of general relativity with regard to the nine Bianchi types and issues of singularities.The situations of vanishing rotation and vanishing shear are treated separately. The homogeneous Bianchi I model is considered as an example of a rotation-free cosmology with anisotropy. It is found in the Newtonian approximation that there are arbitrary functions that need to be given for all time if the initial value problem is to be well-posed, while in the post-Newtonian case there is no such need. For the general case of a perfect fluid only the post-Newtonian theory can satisfactorily describe the effects of pressure. This is in accordance with findings in [7] where the post-Newtonian approximation was applied to homogeneous cosmologies.For a shear-free anisotropic homogeneous cosmology the Newtonian theory of Heckmann and Schücking, [2] is explored. Comparisons with its relativistic and post-Newtonian counterparts are made. In the Newtonian theory solutions exist to which there are no analogues in general relativity. The post-Newtonian approximation may provide a way out.     

Post-Newtonian generation of gravitational waves in a theory of gravity with torsion

We adapt the post-Newtonian gravitational-radiation methods developed within general relativity by Epstein and Wagoner to the gravitation theory with torsion, recently proposed by Hehl et al., and show that the two theories predict in this approximation the same gravitational radiation losses. Since they agree also on the first post-Newtonian level, they are at the present time-observationally-indistinguishable.     

Newtonian and Post-Newtonian Approximations of the k= 0 Friedmann–Robertson–Walker Cosmology

In a previous paper [9], we derived a post-Newtonian approximation to cosmology which, in contrast to former Newtonian and post-Newtonian cosmological theories, has a well-posed initial value problem. In this paper, this new post-Newtonian theory is compared with the fully general relativistic theory, in the context of the k= 0 Friedmann–Robertson–Walker cosmology. It is found that the post-Newtonian theory reproduces the results of its general relativistic counterpart, whilst the Newtonian theory does not.     

New post-Newtonian parameter to test Chern-Simons gravity

We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory.     

Uniqueness of First Order Post-Newtonian Collinear Solutions for Three-Body Problem under a Scalar-Tensor Theory

As a continuing investigation of an earlier work that establishes the collinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System,we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid.The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.     

Relativistic celestial mechanics of binary stars

We present the results of a systematic study of the dynamics of realistic binary systems in the post-Newtonian approximation (PNA) of general relativity. We propose definitions valid in the PNA for the self-angular-momenta of the binary's members, as well as for the angular momentum of their relative orbital motion, and we examine under which conditions they can be considered as constant in the PNA. This enables us to define to the same approximation the plane relative orbital motion. Then we find the form of the differential equations of motion from an integration of which we prove that in the PNA the relative motion is a processing ellipse composed of a basic orbit and a correction, both of which are of post-Newtonian character. Moreover, using the polar equation of the above ellipse we define the elements of the post-Newtonian, relative, basic orbit, we generalize to the PNA the three well-known laws of classical celestial mechanics of Kepler, and we derive the precessional motion of the relative orbit's pericenter. Finally, we compare our method with other methods existing in the literature, and we expose its theoretical and conceptual differences with them.     

The Post-Newtonian Effects of the Rotation of the Central Body on the Motion of the Celestial Body in Three Gravitational Theories

The post-Newtonian effects of the rotation of the central body on the variation of celestial orbital elements are studied according to the post-Newtonian metric theory. The variation of celestial orbital elements caused by the rotation of the central body in three gravitational theories of Einstein, Brans-Dicke and Nordtvedt is obtained by using the method of general perturbation. The resulting effects are the periodic variation of inclination, eccentricity and mean anomaly; the periodic and secular variation of longitudes of periastron and ascending node and mean longitudes of epoch, but the semimajor axis remains unperturbed (no variation). In addition, the obtained theoretical results are applied to the calculation of the post-Newtonian effect of the rotation of the sun on the variation of the orbital elements of planets in solar system. The numerical results are given in nble 1. Finally, the obtained results are discussed and compared with other theories.     

Equations of motion in Rosen's bimetric theory of gravitation

The paper contains an investigation of Rosen's bimetric theory of gravitation in the case of slow velocities and weak fields. Newtonian and post-Newtonian approximations are obtained. The post-Newtonian equation of motion is integrated for an insular system of spherical bodies that move translationally at large mutual distances. It appears that the post-Newtonian law of motion obtained in this way contains terms that depend on the self-energy of the test body (a self-influence phenomenon). It is proved that also in the Einsteinian gravitation this influence is present, but it can be canceled out from the post-Newtonian law of motion if one takes into account the de Donder conditions. The self-influence discovered here seems to be a general gravitation phenomenon, which usually appears in theories of gravitation in the post-Newtonian approximation.     

行星重力的后牛顿近似对卫星作用的估计

将行星重力的广义相对论后牛顿近似应用于木星系统和撞击木星的彗星Shoe maker Levy 9,计算了木星重力的后牛顿改正和它的卫星的进动效应,并与地球月球系统作比较,进行分析和讨论 关键词： 重力的后牛顿近似 木星及其卫星 彗星Shoe maker-Levy 9 广义相对论     

Scalar-tetrad theories of gravity

A general theory of gravitation is constructed using a tetrad and a scalar field. The resulting theory, called a scalar-tetrad theory, does not contain Einstein's or the Brans-Dicke theories as special cases. However, there is a range of scalar-tetrad theories with the same post-Newtonian limit as Einstein's theory. Two particular models are interesting because of their simplicity.     

Calculation of the first nonlinear contribution to the general-relativistic spin-spin interaction for binary systems

We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents the first contribution to the spin-spin interaction due to the nonlinear nature of general relativity and will play an important role in forthcoming gravity wave experiments.     

The black hole and FRW geometries of non-relativistic gravity

We consider the recently proposed non-relativistic Ho?ava–Lifshitz four-dimensional theory of gravity. We study a particular limit of the theory which admits flat Minkowski vacuum and we discuss thoroughly the quadratic fluctuations around it. We find that there are two propagating polarizations of the metric. We then explicitly construct a spherically symmetric, asymptotically flat, black hole solution that represents the analog of the Schwarzschild solution of GR. We show that this theory has the same Newtonian and post-Newtonian limits as GR and thus, it passes the classical tests. We also consider homogeneous and isotropic cosmological solutions and we show that although the equations are identical with GR cosmology, the couplings are constrained by the observed primordial abundance of ⁴He.     

Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part II. Radiation reaction and higher-order divergent terms

We continue the calculation begun in Part I of hydrodynamic equations in general relativity according to Fillers' suggested modification of the iteration scheme of Anderson and DeCanio. We carry out this calculation far enough into the third and fourth iterations to obtain two principal results: First, we obtain a Newtonian-like force equation which is manifestly finite through the leading term of the radiation-reaction force (the 21/2 post-Newtonian approximation). Going beyond the 21/2 PNA, we find, and explicitly present, divergent terms which cannot be canceled out within this scheme. The implications of these results are discussed.     

On the two-body problem in general relativity

We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (∼1/c⁶ beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO and LISA type experiments.     

Gravitational two-body problem—A source theory viewpoint

An analysis of the semirelativistic gravitational two-body problem based on Schwinger's source theory is given. Our treatment is purely classical but nongeometrical. Only the large distance behavior of the gravitational stress tensor is seen to be relevant for order G² contributions. For a gravitational stress tensor that has a pure Newtonian form, only the traceless choice is seen to be consistent with Einstein's theory. We find results in agreement with the earlier results of Einstein, Infeld, and Hoffmann, and Barker and O'Connell for spin-2 graviton exchanges between Dirac particles, and with Börner, Ehlers, and Rudolph for spin precession in theories with arbitrary post-Newtonian parameter γ. The source approach clearly displays the analogy between gravitational interactions and classical electrodynamics. We also discuss the general relationship between the periastron advance and spin-precession frequencies for a class of gravitation theories. Brief estimates of the various spin-precession effects are given for the Hulse-Taylor pulsar.     

L?(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。 关键词：     

Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order

The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values xi=-9871/9240, kappa=0, and zeta=-7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciphering the signals in the current network of gravitational wave detectors.     

Light Propagation in the Second post-Newtonian Approximation of Scalar-Tensor Theory of Gravity

In this paper, we use the metric coefficients and the equation of motion obtained in the second post-Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GAIA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-arcsecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.