zbMATH — the first resource for mathematics

Minkowski space as a basis for a physical theory of gravitation. (English. Russian original) Zbl 0576.53072
Theor. Math. Phys. 60, 635-638 (1984); translation from Teor. Mat. Fiz. 60, No. 1, 3-8 (1984).
The authors propose a version of gravitation theory based on the bimetric formalism of N. Rosen with a flat background metric \(\gamma_{ik}\) which is interpreted as a true spacetime metric while the Riemannian metric \(g_{ik}\) is considered as a sum, \(\gamma_{ik}+\Phi_{ik}\), where \(\Phi_{ik}\) is the gravitational field potential. \(\gamma_{ik}\) is not necessarily taken in Cartesian coordinates so that the corresponding covariant derivatives are to be used. The gravitational Lagrangian is that of Hilbert, and a divergence term is as usually extracted.
The authors make a statement that ”in general relativity, the principle of relativity is not satisfied” while in the bimetric approach, ”there is a principle of relativity, which states that it is not possible by any physical process (including gravitational processes) to establish whether one is in a state of rest or uniform rectilinear motion”. The auxiliary conditions on \(\Phi_{ik}\) are in fact those of harmonicity adapted to this bimetric approach. But the authors also impose a condition of asymptotic behaviour of \(\Phi_{ik}\) for insular systems and insist that this condition is a universal one thus excluding all but flat-three-space models in cosmology. In this case, there always exist all usual conservation laws of the special relativity [cf. also A. Papapetrou, Proc. R. Ir. Acad., Sect. A 52, 11-23 (1948; Zbl 0037.421) though this author does not deviate from the standard interpretation of general relativity].
Reviewer: N.Mitskievich

53C80 Applications of global differential geometry to the sciences
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
Full Text: DOI
[1] A. A. Logunov et al., Teor. Mat. Fiz.,40, 291 (1979).
[2] V. I. Denisov and A. A. Logunov, Teor. Mat. Fiz.,50, 3 (1982); V. I. Denisov and A. A. Logunov, Fiz. Elem. Chastits At. Yadra,13, 753 (1982); V. I. Denisov and A. A. Logunov, Itogi Nauki Tekh., Seriya ?Sovremennye Problemy Matematiki?,21, 3 (1982).
[3] N. Rosen, Phys. Rev.,57, 147 (1940). · Zbl 0023.18705 · doi:10.1103/PhysRev.57.147
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.