Abstract
Using a fast-motion approximation method we obtain the second-order gravitational field and equations of motion for two pointlike objects in algebraically closed form. A regularization procedure is used which is shown to guarantee the consistency of the approximation scheme. The equations of motion are then transformed within the framework of relativistic predictive mechanics into a system of ordinary differential equations.
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Bel, L., Damour, T., Deruelle, N. et al. Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity. Gen Relat Gravit 13, 963–1004 (1981). https://doi.org/10.1007/BF00756073
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DOI: https://doi.org/10.1007/BF00756073