On the motion of test particles in the field of a plane gravitational wave

The motion of test particles in the field of a plane gravitational wave is studied in order to derive some general properties of such motion, especially the possibilities of repeated meetings of two inertially moving particles.The work was done at Moscow State University, Moscow.     

Chaos feature of test particle in the gravitational field with a quadrupole

In this paper we investigate the dynamics of a test particle in the gravitational field with a quadrupole. By constructing Poincaré sections for different values of the parameters and initial conditions, we find a chaotic evolution. From these Poincaré sections, we further confirm that the chaotic evolution of the test particle originates from the quadrupole.     

Massless spinning test particles in a gravitational field

The classical equations of motion of a massless spinning test particle are derived as a limiting case of Mathisson-Papapetrou equations. It is shown that when a particular supplementary condition is assumed the particle follows a null geodesic and the spin is either parallel or antiparallel to the direction of motion. Moreover, the helicity is conserved in an orientable spacetime. The equations of the propagation of the momentum vector and the spin tensor along the trajectory are given and further implications of the solution are discussed.     

On the intrinsic entropy of the gravitational field

I show that in linearized general relativity it is impossible to construct a detector by the use of which the quantum state of the linearized gravitational field could be reliably determined. This is because there is no material satisfying the positive energy condition which can serve as a good conductor or absorber of gravitational radiation over a finite range of frequencies. If this property is true of the full theory then one can conclude that a certain proportion of both the energy and information carried by a gravitational wave is irreversibly lost, and that there is a correspondingintrinsic entropy associated with any distribution of gravitational radiation.     

Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test

We deal with the test of the general relativistic gravitomagnetic Lense-Thirring effect currently being conducted in the Earth’s gravitational field with the combined nodes Ω of the laser-ranged geodetic satellites LAGEOS and LAGEOS II. One of the most important sources of systematic uncertainty on the orbits of the LAGEOS satellites, with respect to the Lense-Thirring signature, is the bias due to the even zonal harmonic coefficients J _? of the multipolar expansion of the Earth’s geopotential which account for the departures from sphericity of the terrestrial gravitational potential induced by the centrifugal effects of its diurnal rotation. The issue addressed here is: are the so far published evaluations of such a systematic error reliable and realistic? The answer is negative. Indeed, if the difference ΔJ _? among the even zonals estimated in different global solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, ITG-Grace02, ITG-Grace03s, JEM01-RL03B, EGM2008, AIUB-GRACE01S) is assumed for the uncertainties δJ _? instead of using their more-or-less calibrated covariances \(\sigma _{J_\ell } \), it turns out that the systematic error δμ in the Lense-Thirring measurement is about 3 to 4 times larger than in the evaluations so far published based on the use of the covariances of one model at a time separately, amounting up to 37% for the pair EIGEN-GRACE02S/ITG-Grace03s. The comparison among the other recent GRACE-based models yields bias as large as about 25–30%. The major discrepancies still occur for J ₄; J ₆ and J ₈, which are just to which the zonals the combined LAGEOS/LAGOES II nodes are most sensitive.     

On quantum field theory in gravitational background

We discuss quantum fields on Riemannian space-time. A principle of local definiteness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows us to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non-stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non-inertial motion are added.     

On the gravitational field of a massless particle

The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a -like singularity and is exactly of Petrov typeN.This work was supported in part by Fonds zur Förderung der Wissenschaftlichen Forschung.     

On the effect of spin on the gravitational field

Using a solution of Trautman's recently formulated Einstein-Cartan equations, it is shown that if an isolated body is embedded in an expanding universe consisting of a dust of spinning particles, then the local gravitational field of the body is influenced by spin, even when the cosmological constant is neglected.     

On the exterior gravitational field of a mass with a multipole moment

Recently, Gutsunaev and Manko [6] presented a procedure for obtaining new static axisymmetric solutions of Einstein's vacuum field equations from a known one. We show that this procedure is based on the property that the derivatives of a harmonic function are harmonic. The special case of a metric with mass and quadrupole moment is investigated and compared with the Erez-Rosen metric.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

On the gravitational field acting as an optical medium

Given a curved space-time with a metric tensorg _ij, Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.When optical phenomena are considered, this medium turns out to be equivalent to the gravitational field. Optical phenomena in various gravitational fields are analysed and we find that the language of classical optics for the equivalent medium is as suitable as that of Riemannian geometry.This work was started at the Department of Applied Mathematics and Theoretical Physics, Cambridge, England.     

On the gravitational field of a plane plate in general relativity

It is shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry. As a consequence, the boundaries of the plate are joined with qualitatively different vacuum solutions on both sides of the plate.     

Neutron interferometry in gravitational field with torsion

We consider the possibility of finding experimental evidence of the fifth force with the measurement of a phase shift of neutron beams via an interferometric apparatus and also a possible rotation of the polarization plane of polarized neutron beams when torsion is introduced in a gravitational field.