Structure of the generalized momentum of a test charged particle and the inverse problem in general relativity theory

The inverse problem is solved in general relativity theory (GRT) consisting in determining the metric and potentials of an electromagnetic field by their values in the nonsingular point of the V4 space and present functions, being the generalized momenta of a test charged particle. The Hamilton-Jacobi equation for a test charged particle in GRT is used. The general form of the generalized momentum dependence on the initial values is determined. It is noted that the inverse problem solution of dynamics in GRT contains arbitrariness which depends on the choice of the metric and potential values of the electromagnetic field in the nonsingular point