Spherically symmetric solution in the theory of gravitation based on Minkowski space.

*(English. Russian original)*Zbl 0576.53073
Theor. Math. Phys. 60, 739-743 (1984); translation from Teor. Mat. Fiz. 60, No. 2, 163-168 (1984).

In the bimetric theory formulated by the same authors [see the preceding review], a spherically symmetric vacuum solution for \(\Phi_{ik}\) is now deduced, being of the same form as the Schwarzschild solution in general relativity though the radial coordinate of the flat background metric is connected with the usual radial Schwarzschild’s coordinate by a complicated relation which is even not written otherwise than asymptotically. However the authors insist that their theory does not lead to any horizon-like singularity. The usual conclusion about the total inertial mass of the system is also deduced.

Reviewer: N.Mitskievich

##### MSC:

53C80 | Applications of global differential geometry to the sciences |

83C15 | Exact solutions to problems in general relativity and gravitational theory |

83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |

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\textit{A. A. Vlasov} and \textit{A. A. Logunov}, Theor. Math. Phys. 60, 739--743 (1984; Zbl 0576.53073); translation from Teor. Mat. Fiz. 60, No. 2, 163--168 (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); Fiz. Elem. Chastits At. Yadra,13, 757 (1982); in: Modern Problems of Mathematics, Vol. 21 (Reviews of Science and Technology) [in Russian], VINITI, Moscow (1982), pp. 3-216. |

[3] | A. A. Logunov and A. A. Vlasov, Teor. Mat. Fiz.,60, 3 (1984). |

[4] | N. Rosen, Phys. Rev.,57, 147 (1940); Ann. Phys. (N.YY.),22, 1 (1963). · Zbl 0023.18705 · doi:10.1103/PhysRev.57.147 |

[5] | S. Weinberg, Gravitation and Cosmology, Wiley, New York (1972). |

[6] | E. I. Molseev and V. A. Sadovnichii, Solution of a Nonlinear Equation in the Theory of Gravitation Based on Minkowski Space [in Russian], Moscow State University (1984). |

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