Author(s)

Valery V. Vasiliev, Leonid V. Fedorov

Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia.

The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.

General Relativity, Gravitation Constant, Linearized Equations, Spherically Symmetric Problem

Vasiliev, V. and Fedorov, L. (2020) Linearized Equations of General Relativity and the Problem of Reduction to the Newton Theory. Journal of Modern Physics, 11, 221-236. doi: 10.4236/jmp.2020.112014.