Inverse problems of the general-relativistic mechanics of test bodies and applications to general relativity

In a generally relativistic framework, we pose and solve problems of reconstructing a tensor force field of Lorentz type and a scalar force field V(xⁱ) from a given metric of a four-dimensional Riemannian space-time and given properties of the motion of test bodies in this space. We solve the problem of finding the potentials g_i of the gravitational field from known tensor force field F_i = F_i and from given properties of the motion of bodies in the gravitational field which is being sought. The functional arbitrariness in the solution of these inverse problems is established. Applications of the results to the general theory of relativity are demonstrated and reveal new possibilities of experimental determination of physical fields from their effect on test bodies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–29, October, 1980.