静态球对称引力场中光线偏折的几何算法

光线的引力偏折和光在介质中的折射有统一的地方,本文采用几何光学的方法讨论星光掠过太阳时的偏折角度,所得结果和经典文献一致.     

The gravitational field of static spherically symmetric bodies

The study of a previously proposed theory of gravitation [Petry, W. (1979).Gen. Rel. Grav.,10, 599; (1981).Ibid,13, 865] is continued. The field equations are given in a simple covariant form. For a perfect fluid with pressure the static spherically symmetric solutions of the gravitation theory are studied. Inertial and gravitational mass are identical. The solutions agree with the corresponding results of the theory of general relativity up to high order in the coupling constant. Under some natural conditions the solutions of a static spherically symmetric body are not singular.     

Equations of motion of test bodies in a spherically symmetric,static gravitational field

We consider a class of theories of gravity in which the motion of test particles is governed by the path equation (with respect to a general affine connection Г). When we restrict attention to a spherically symmetric, static gravitational field, the path equation is characterized by three arbitrary functions of the gravitational field (as opposed to two in the case of metric theories where Г={ }). We find that there are essentially only two constraints on the three functions by appealing to solar system experiments. Therefore, we must supplement the equation of motion with other physical laws to obtain a value for the third arbitrary function (this, of course, is not necessary in the case of metric theories). If we consider theories in which both Г andg play a physical role we find in certain circumstances that this “third” condition is sufficient to prove that the theories under investigation reduce to their “metric” form.     

The energy-momentum tensor of a static gravitational field

The method of a tetrad field proposed by Rayski was used to determine the energy-momentum tensor for an approximate solution of the Einstein equations in the static case, from which it follows that the static gravitational field has non-zero mass but zero momentum, as was to be expected.In conclusion the author thanks P. Burcev for fruitful discussions and great interest in this work.     

External gravitational field of a non-static spherically symmetric body

It is shown that in the field theory of gravitation, the external gravitational field of a non-static spherically symmetric source described by a diagonal metric tensor can be static only.     

Homotopically nontrivial solutions for a spherically symmetric gravitational field

The structure of kink solutions to the Einstein field equations is discussed and the most general form of spherically symmetric kink metric is constructed. A number of fluid solutions are investigated and an imperfect fluid solution with nonzero heat conduction is presented.     

Black-body radiation and thermal equilibrium in a static gravitational field

The black-body radiation law in the presence of a static gravitational field is obtained by extending the usual expression valid in a flat space-time region with the help of a purely mechanical argument. The result allows us to recover the dependence of the proper local temperature on position in such a field.     

Spectrum of stationary electromagnetic radiation in a static gravitational field

From the equation of continuity, an equation is derived for the change in the spectrum of radiation stationary in a static gravitational field, as measured by local observers in their proper frame. It is shown that an isotropic solution always exists in which the energy density per unit frequency interval is ³ times an arbitrary function of .     

On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.     

Point charge in a static,spherically symmetric Brans-Dicke field

We determine in closed form the electrostatic potential of a point test charge held at rest in a static, spherically symmetric Brans-Dicke field. This result is a generalization of the previously obtained expression for the potential of a test charge at rest near a Schwarzschild black hole. Moreover, our solution is valid for the coupled gravitational and massless scalar fields.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

The static gravitational field near spatial infinity I

A static solution to Einstein's equations, which is asymptotically flat near spatial infinity, is shown to be asymptotically Schwarzschildian. As an application of this result we prove a technical lemma on the existence of asymptotically flat harmonic coordinates near infinity.     

Semiclassical dynamics of Dirac particles interacting with a static gravitational field

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy–Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian previously found by other authors. But our formalism provides for another effect, namely, the spin hall effect, which was not predicted before in this context.     

The electrostatic and gravitational field of spherically symmetric objects

The electrostatic and gravitational fields of an extended spherically symmetric object is presented. The limit to a point-like object is discussed for Born-Infeld type of electrodynamics and it is shown, that the extreme Reissner-Nordstrøm field, where no event horizon occurs, is unphysical.     

On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a “soundproof” Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.     

A static three-center solution to Einstein's gravitational field equations

In this paper the physical situation of three collinear, axisymmetric masses is studied within the framework of Einstein's general theory of relativity. A solution is found, and the feasibility of the existence of coupled negative-positive masses is demonstrated in direct correspondence to such a feasibility in Newtonian theory.