Lagrangians forn point masses at the second post-Newtonian approximation of general relativity |
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Authors: | Thibault Damour Gerhard Schäfer |
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Institution: | (1) Groupe d'Astrophysique Relativiste, Equipe de Recherche du C.N.R.S., No. 176, Observatoire de Paris-Meudon, 92195 Meudon Principal Cédex, France;(2) Institut für Astrophysik, Max-Planck-Institut für Physik und Astrophysik, D-8046 Garching bei München, Federal Republic of Germany;(3) Fakultät für Physik der Universität Konstanz, Postfach 5560, D-7750 Konstanz, Federal Republic of Germany |
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Abstract: | We study the effect of an infinitesimal coordinate transformation on the Lagrangian and on the metric functional of a system ofn point masses. We show how to compute the Lagrangians ofn point masses at the second postNewtonian 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, but excludes most other coordinate systems used in the literature (notably the harmonic one). |
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