Other
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993acppb..24..927c&link_type=abstract
Acta Phys. Pol., B, Vol. 24, No. 5, p. 927 - 950
Other
3
Scientific paper
Equations of gravitation in the Lobachevsky space are formulated. The problem of the gravitational field of a point mass in the Lobachevsky space is solved. In the Newtonian (nonrelativistic) case, this problem was posed and solved by Lobachevsky himself. In the relativistic case, one should first find adequate equations for the metric describing the gravitational field and then find their solutions. These equations are found by the author on the basis of the theory, developed by him, with two affine connections; one called Christoffel and the other, background. The latter is given by the equations of motion of free material particle in the Lobachevsky space. It is independent of the light velocity c. The static spherically symmetric metric found here depends on the ratio of the gravitational radius γMc-2 of mass M to the Lobachevsky constant k for the visible world. In the limit k→-∞ it turns into the well known Schwarzschild metric. The world line of a planet is geodesic with respect to this metric. The relativistic Kepler problem in the Lobachevsky space is reduced to a nonlinear differential equation.
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