The application of methods of the theory of ordinary differential equations Fuchs class to study the properties of solutions of the Klein–Gordon equations in the General Relativistic Theory

The properties of solutions of the Klein–Gordon equations for various metrics of the general theory of relativity are considered. It is shown that the presence of singular points of the metric leads to qualitative rearrangement solutions of this equation, and the desingularization of solutions by a choice of a new metric requires a priori assumptions that can lead to a formally mathematically correct, but paradoxical physical meaning results.