| Abstrakt: |
It is shown that, if (a) the gravitational field is represented by the metric tensor of a Riemann space, (b) the geodesic hypothesis is admitted, (c) it is assumed that, for a particle moving in a scalar gravitational field, this last postulate must give, by approximation, the Hamilton principle for this particle in special relativity, then a metric tensor is obtained with some interesting properties (no assumptions are made about field equations). The geodesic hypothesis, with the Lorentz transformation of this metric tensor, gives, by approximation, the Hamilton principle, with the Lagrangian corresponding in special relativity to a particle in a vector field. Moreover, the equations of motion in a Riemann space, as they follow from the geodesic postulate, in terms of associated coordinates, give, by approximation, an expression in complete analogy to that of the Lorentz force. Hence, the vector-field theory of gravitation of the Maxwell-Lorentz kind (as electrodynamics, because of the formal analogy between the two theories) is obtained as a weak field approximation of a description of gravitational (electromagnetic) interaction by a metric tensor in a Riemann space (except the field equations, an issue that we do not touch, so far). |
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