Lagrangians for n point masses at the second post-Newtonian approximation of general relativity (Q1060576)

We study the effect of an infinitesimal coordinate transformation on the Lagrangian and on the metric functional of a system of n point masses. We show how to compute the Lagrangians of n point masses at the second post- Newtonian approximation of general relativity in different coordinate systems. The Lagrangians are shown to depend on the accelerations except in a special class of coordinates. This class includes the coordinates associated with the canonical formalism of Arnowitt, Deser, and Misner [in: \textit{L.Witten} (ed.), Gravitation: An introduction to current research (1962; Zbl 0115.431)], but excludes most other coordinate systems used in the literature (notably the harmonic one).