Equations of motion in the theory of gravitational perturbations

Abstract

In the two lowest orders of the fast motion approximation for gravitational perturbations the equations of motion for a system of point particles are derived from the (slightly modified) equations of motion for a perfect compressible fluid by a transition from small drops to pointlike particles. In the first order equations the singular terms arising in the limit l → 0 ( l is the diameter of a drop), which do not cancel out because of the stability condition, are removed by a mass renormalization. Radiation damping terms occur like those in electrodynamics. In the second approximation there are needed two subtractions: one for the mass and one for the coupling constant. The “damping terms” in the second order equation of motion are symmetric under time reversal.