What Happens in the Vicinity of the Schwarzschild Sphere When Nonzero Graviton Rest Mass Is Present

In this paper a solution for a static spherically symmetric body is thoroughly considered in the framework of the Relativistic Theory of Gravitation. By the comparison of this solution with the Schwarzschild solution in General Relativity their substantial difference is established in the region close to the Schwarzschild sphere. Just this difference excludes the possibility of collapse to form “black holes”. The given problem was considered for the first time in the Relativistic Theory of Gravitation (RTG) in paper [1], where it was established that in vacuum the metric coefficient g00 of the effective Riemannian space was not equal to zero on the Schwarzschild sphere, whereas g11 had a pole. These changes which have arisen in the theory because of the graviton mass result in a “bounce” effect of the falling particles and light from a singularity on the Schwarzschild spere, and consequently, in the absence of “black holes”. Later in paper [2] an in-depth study of this problem in the RTG was conducted which updated a number of points, but at the same time showed, that the “bounce” took place close to the Schwarzschild sphere. In view of importance of this problem we again come back to its analysis with the purpose of showing in a simpler and clearer way that in that point in vacuum where the metric coefficient of effective Riemannian space g11 has a pole, another metric coefficient g00 will not vanish. 1 In RTG [3] the gravitational field is considered as a physical field in the Minkowski space. The source of this field is the universal conserved density of the energy-momentum tensor of the entire matter including the gravitational field. This circumstance results in the emerging of the effective Riemannian space because of the presence of the gravitational field. The motion of matter in the Minkowski space under the influence of the gravitational field proceeds in the same way as if it moved in the effective Riemannian space. The field approach to gravitation with necessity requires the introduction of the graviton rest mass. In RTG, as opposed to the General Relativity Theory (GRT), the inertial reference frames are present and consequently the acceleration has an absolute meaning. The forces of inertia and gravity are separated, as they are of completely different nature. The Special Relativity Principle holds for all the physical fields, including the gravitational one. It follows from this theory that gravitational forces in the Newtonian approximation are the forces of attraction. Since a physical field can be described in one coordinate system, it means, that the effective Riemannian space has a simple topology and is set in one chart. In RTG the Mach Principle will be realised — an inertial reference frame is determined by the distribution of matter. In this theory the Correspondence Principle takes place: after switching off the gravitational field the curvature of space disappears, and we find ourselves in the Minkowski space in the coordinate system prescribed earlier. The RTG equations look like R ν − 1 2 δ νR + 1 2 ( mc h̄ )2 ( δ ν + g γαν − 1 2 δ ν g γαβ ) = κT μ ν , (1) Dμg̃ μν = 0 . (2) Here g̃ = √−ggμν , g = det gμν , R ν is the Ricci tensor, κ = 8πG c , G is the gravitational constant, Dμ is the covariant derivative in the Minkowski space, γμν(x) is the metric tensor of the Minkowski space in arbitrary curvilinear coordinates. Equations (1) and (2) are covariant under arbitrary coordinate transformations with a nonzero Jacobian. They are also Lorentz invariant under transformations from one inertial system in Galilean coordinates to another. Equations (2) eliminate representations corresponding to spins 1 and 0 for a tensor field, leaving only the representations with spins 2 and 0. The equations of motion of matter are the consequents of equations (1) and (2).