Example of a relativistic two-body problem

The problem of the relativization of the Newton equations for two bodies is solved in the case when the interaction potential is proportional to the distance between the bodies. The formulas for angular momentum and momentum vectors are obtained. Considered forces of two body interaction are such that the world trajectories of the bodies are asymptotic lines having a constant curvature on the minimum surface Σ. The interaction forces are transmitted by the particles which world trajectories form the isotropic network of the Σ surface. Such particles have zero rest mass when necessary. The boundary conditions for a joint surface are described. The minimum surface with the specified asymptotic line of constant curvature is obtained