Generalization of the Bohlin–Arnold Theorem and Its Application in General Relativity Theory

Abstract

The general Bohlin transforms are used to switch between the solutions of the problem on the motion of a test body with different spherically symmetric potentials. It has been established that the parabolic Bohlin transforms are grouped in character. The Bohlin transforms describing the change from a simple exponential potential to a generalized polynomial potential have been obtained in the general form. With specific, widely known spherically symmetric metrics used as an example, it has been shown that these transforms can be used to determine the trajectory of a test body in general relativity theory.