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Solutions of Einstein's Equations: Techniques and Results pp 367–391Cite as

The Newtonian limit

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Part of the book series: Lecture Notes in Physics ((LNP,volume 205))

Abstract

We discuss in detail the development of the Newtonian and post-Newtonian approximations to general relativity. By using an initial-value approach, we are able to show that the post-Newtonian hierarchy through gravitational-radiation-reaction order is an asymptotic approximation to general relativity, thereby verifying the validity of the quadrupole formula for radiation reaction. We also show with equal rigor that the radiation from nearly-Newtonian systems obeys the far-field quadrupole formula (Landau-Lifshitz formula).There are no divergent terms in these approximations at any order, although logarithmic terms in the expansion parameter do appear at high order. We discuss the relationships of observables to post-Newtonian quantities by the method of osculating Newtonian orbits. Finally we discuss the role exact solutions may play in shedding light on some of these questions.

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References

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Authors and Affiliations

  1. Department of Applied Mathematics and Astronomy, University College, P.O. Box 78, Cardiff, U.K.

    Bernard F. Schutz

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  1. Bernard F. Schutz
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C. Hoenselaers W. Dietz

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© 1984 Springer-Verlag

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Schutz, B.F. (1984). The Newtonian limit. In: Hoenselaers, C., Dietz, W. (eds) Solutions of Einstein's Equations: Techniques and Results. Lecture Notes in Physics, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13366-6_17

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  • DOI: https://doi.org/10.1007/3-540-13366-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13366-7

  • Online ISBN: 978-3-540-38922-4

  • eBook Packages: Springer Book Archive

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