To the Solution of a Spherically Symmetric Problem of General Relativity

Abstract

The paper is devoted to the spherically symmetric problem of General Relativity. Existing solutions obtained by K. Schwarzschild and V. Fock are presented and discussed. A special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. The solution of the Einstein equations for the empty space with this geometry coincides with the solution in Gullstand-Painlever coordinates. In application to the found solution, the problem of the light trajectory deviation in the vicinity of Sun and the problem of escape velocity are discussed.