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].

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

##### MSC:

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 |

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\textit{A. A. Logunov} and \textit{A. A. Vlasov}, Theor. Math. Phys. 60, 635--638 (1984; Zbl 0576.53072); translation from Teor. Mat. Fiz. 60, No. 1, 3--8 (1984)

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##### References:

[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 |

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