ON SINGLE-TIME METHODS IN RELATIVISTIC GRAVITY DYNAMICS
A short outline of revived methods of an action-at-a-distance description of interacting particles is given. A new approach to the problem of motion in relativistic gravity is discussed. The approach makes an essential use of the predictive relativistic mechanics method with some phenomenological assumptions as to the character of relativistic “forces”. The technique of the construction of the approximate solutions for the Currie-Hill equations is proposed. Some recurrent conditions for these solutions are proved to be necessary and sufficient. The generalized Poincaré-invariant equations of motion are derived in post-Newtonian approximations of the phenomenological formulation of the relativistic action-at-a-distance gravity for the closed system of structureless particles. Connections of these equations with those of the Lagrangian description are discussed.