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Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity

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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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Author notes

  1. Jesus Martin

    Present address: Universidad de Salamanca, Salamanca, Spain

Authors and Affiliations

  1. Equipe de Recherche Associée au C.N.R.S. No. 533, Laboratoire de Gravitation et Cosmologie Relativistes, Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75231, Paris Cedex 05, France

    Luis Bel & Nathalie Deruelle

  2. Equipe de Recherche du C.N.R.S. No. 176, Groupe d'Astrophysique Relativiste, Observatoire de Meudon, 92190, Meudon, France

    Thibaut Damour

  3. Universidad del Pais Vasco, San Sebastian, Spain

    Jesus Ibanez & Jesus Martin

Authors
  1. Luis Bel
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  2. Thibaut Damour
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  3. Nathalie Deruelle
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  4. Jesus Ibanez
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  5. Jesus Martin
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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

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