Newtonian and post-Newtonian approximations are asymptotic to general relativity
A precise definition of the Newtonian and post-Newtonian hierarchy of approximations to general relativity is given by studying a C/sup infinity/ sequence of solutions to Einstein's equations that is defined by initial data having the Newtonian scaling property: v/sup i/approx.epsilon, rhoapprox.epsilon/sup 2/, papprox.epsilon/sup 4/, where epsilon is the parameter along the sequence. We map one solution in the sequence to another by identifying them at constant spatial position x/sup i/ and Newtonian dynamical time tau = epsilont. This mapping defines a congruence parametrized by epsilon, 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.
- Research Organization:
- Department of Applied Mathematics and Astronomy, University College, Cardiff, United Kingdom
- OSTI ID:
- 5425650
- Journal Information:
- Phys. Rev. D; (United States), Vol. 28:10
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GENERAL RELATIVITY THEORY
EINSTEIN FIELD EQUATIONS
BINARY STARS
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GRAVITATIONAL FIELDS
LIGHT CONE
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645400* - High Energy Physics- Field Theory
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation