Chapter

Foundations of the post‐Newtonian approximation

H. Asada, T. Futamase and P. A. Hogan

in Equations of Motion in General Relativity

Published in print December 2010 | ISBN: 9780199584109
Published online January 2011 | e-ISBN: 9780191723421 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199584109.003.0002

Series: International Series of Monographs on Physics

Foundations of the post‐Newtonian approximation

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The strong field point particle limit is defined, the surface integral approach to the evaluation of the equations of motion is described and the scalings of the matter and field variables on an initial space‐like hypersurface are discussed. The Newtonian velocity‐momentum relation and the Newtonian equations of motion for extended bodies are re‐visited and the equations of motion in the first post Newtonian (PN) approximation are obtained and their derivation carefully analyzed. The spin‐orbit coupling force, the quadrupole‐orbit coupling force, the spin‐spin coupling force and the spin geodesic precession equation are calculated to lowest order. These calculations are described in Appendix B which, in addition to Appendix A, is directly relevant to this chapter.

Keywords: strong field; point particle limit; Lorentz contraction; multipole moments

Chapter.  17421 words. 

Subjects: Mathematical and Statistical Physics

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