On the Relations Between Field Equations and Equations of Motion in Newtonian 
and Einsteinian Gravity

Ehlers, Jürgen

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On the Relations Between Field Equations and Equations of Motion in Newtonian and Einsteinian Gravity

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Ehlers, Jürgen
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Ehlers, J. (2008). On the Relations Between Field Equations and Equations of Motion in Newtonian and Einsteinian Gravity. Acta Physica Polonica B Proceedings Supplement, 39(1), 123-131.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-63B8-C

Abstract

A pseudo-field theoretic reformulation of the Newton--Euler dynamics of isolated, gravitating fluids is given. The basic equations of that theory are shown to be regular limits of Einstein's gravitational field equation. It is reviewed how the equations of motion for mass points can be obtained as approximations from those for extended bodies without use of a regularisation to remove infinities. Finally Einstein's (1916--1918) approximation method is revived; its similarity to Newtonian theory suggests the possibility of avoiding infinities also in General Relativity.