Incompatibility of the Tolman solution for dust-like matter with the causality principle

摘要

The article considers the problem on the possibility of collapse of dust-like matter within the framework of the general theory of relativity (GTR). In the physical mechanism of the cessation of gravitational compression and the following expansion is described in detail within the framework of the RTG. It is related to the elasticity of the field arising due to the presence of the energy-momentum tensor of the gravitational field. The Tolman solution for dust-like matter does not satisfy the Hilbert causality principle. For this exact reason, it is impossible to assert the reality of collapse even for dust-like matter on the basis of the Tolman model. From the information stated above, it is possible to draw a general conclusion: the physical gravitational fields obtained by the solution of the Hilbert-Einstein equations with taking into account the Hilbert causality principle cannot impart physical velocity equal to the velocity of light in a limited proper time to the probe solids moving with a certain initial velocity along a geodetic line.