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.
References
[1]
Vasiliev, V.V. (1997) Mechanics of Solids, 3, 150-155.
[2]
Landau, L.D. and Lifshits, E.M. (1988) Field Theory. Nauka, Moscow. (In Russian)
[3]
Singe, J.L. (1960) Relativity: The General Theory. North Holland, Amsterdam.
[4]
Weinberg, S. (1972) Gravitation and Cosmology. John Wiley and Sons, Inc., New York.
[5]
Vasiliev, V.V. and Fedorov, L.V. (2019) Journal of Modern Physics, 10, 1401-1415. https://doi.org/10.4236/jmp.2019.1012093
[6]
Vasiliev, V.V. (2017) Journal of Modern Physics, 8, 1087-1100. https://doi.org/10.4236/jmp.2017.87070
[7]
Arroyo-Torres, D., Wittkovski, M., Marcaide, J.M. and Hauschildt, P.H. (2013) Astronomy and Astrophysics, 554, A76. https://doi.org/10.1051/0004-6361/201220920
[8]
Vasiliev, V.V. and Fedorov, L.V. (2018) Journal of Modern Physics, 9, 2482-2494. https://doi.org/10.4236/jmp.2018.914160
[9]
Logunov, A.A. (2006) Relativistic Theory of Gravitation. Nauka, Moscow. (In Russian)
[10]
Froeschle, M., Mignard, F. and Arenou, F. (1997) Determination of the PPN Parameter γ with the Hipparcos Data. Proceedings of the ESA Symposium ‘Hipparcos Venice 97’ Italy, 13-16 May 1997, ESA SP-402, 49-52.
