A. I. Nikishov

This paper shows that when the velocities of particles in a source are small in comparison with the velocity of light any source generates soft gravitation

The author compares, in the Born approximation, the cross sections for graviton scattering on Newtonian center in three cases using 1) a three-graviton ver

The theory of sources predicts that in the G2-approximationa dependence of the external metric of a sphere on the radius of a material sphere (as well as on its energy-momentum tensor) appears. We...

Applying the theory of sources I consider the consequences of using field theoretical 3- graviton vertex instead of the vertex of general relativity. As an example I look for the lowest nonlinear...

The metric of spherically symmetric ball of ideal incompressible liquid is considered in G²-approximation with the help of the theory of sources. Using the integral equations of this theory gives the exterior metric depending upon the radius b of the ball of matter in some terms proportional to G².

I examine the $G^2$-approximation of Schwarzschild solution from the viewpoint of theory of sources. The method suggests the following definition of the privileged coordinate system: it is a system in which in each approximation the gauge degrees of freedom are put to zero, i.e. the metric is formed solely by sources. I calculate the metric in this system. In $G^2$-approximation the exterior metric has the term which is of the form of a gauge function. Considering it as such I have the agreement with Schwarzschild metric. But I cannot consider it as a gauge function because it is generated by sources. It should be observable. It is proportional to the radius of matter ball and seems violate the Birckhoff theorem.

In general, the force is defined as the derivative of the particle momentum with respect to the proper time. The work of this force during movement of a particle in a constant gravitational field is not consistent with the energy conservation law. The consistency takes place only if the force is defined as the derivative of the momentum with respect to the world time. In our opinion, exactly this force is measured by the spring balance keeping the particle at rest in a constant gravitational field.

Sums of Kapteyn series of several types are obtained and relations between them are found. Special attention is paid to series whose sums are expressed in terms of transcendent functions. Their asymptotics are determined. In some cases, integral representations were obtained and reduced to the form convenient for numerical calculations. The electron lifetime in a constant electromagnetic field before photon emission is determined. It was indicated that this time increases with the ultrarelativistic electron energy in a strong constant field.

The force in the equation of motion of a particle should be in accordance with energy conservation in a constant gravitational field. It turns out that this is possible only if the force is given by the change of momentum per unit of coordinate (not proper) time. We discuss the consequences of this fact. In particular it turns out that the spring balance, which keeps the body at rest in (strong) gravitation field, shows the finite value even at infinitely close approach to horizons of black holes, if they exist in Nature.