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  Newtonian and post-Newtonian approximations are asymptotic to general relativity

Futamase, T., & Schutz, B. F. (1983). Newtonian and post-Newtonian approximations are asymptotic to general relativity. Physical Review D, 28(10), 2363-2372. doi:10.1103/PhysRevD.28.2363.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-0EF0-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-0EF3-E
Genre: Journal Article

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Futamase, Toshifumi1, Author
Schutz, Bernard F.2, 3, Author              
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1External Organizations, Department of Applied Mathematics and Astronomy, University College, Cardiff, United Kingdom, ou_persistent22              
2Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24013              
3External Organizations, Max Planck Institut für Physik und Astrophysik, Garching bei München, Germany and Department of Applied Mathematics and Astronomy, University College, Cardiff, United Kingdom, ou_persistent22              

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 Abstract: A precise definition of the Newtonian and post-Newtonian hierarchy of approximations to general relativity is given by studying a C∞ sequence of solutions to Einstein's equations that is defined by initial data having the Newtonian scaling property: vi∼ε, ρ∼ε2, p∼ε4, where ε is the parameter along the sequence. We map one solution in the sequence to another by identifying them at constant spatial position xi and Newtonian dynamical time τ=εt. This mapping defines a congruence parametrized by ε, and the various post-Newtonian approximations emerge as derivatives of the relativistic solutions along this congruence. We thereby show for the first time that the approximations are genuine asymptotic approximations to general relativity. The proof is given in detail up to first post-Newtonian order, but is easily extended. The results will be applied in the following paper to radiation reaction in binary star systems, to give a proof of the validity of the "quadrupole formula" free from any divergences.

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 Dates: 1983-11-15
 Publication Status: Published in print
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 28 (10) Sequence Number: - Start / End Page: 2363 - 2372 Identifier: ISSN: 1089-4918