Living Reviews in Relativity

"The Post-Newtonian Approximation for Relativistic Compact Binaries"
Toshifumi Futamase and Yousuke Itoh  

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1 Introduction
1.1 Gravitational wave detection and post-Newtonian approximation
1.2 Post-Newtonian equations of motion
1.3 Plan of this paper
2 Foundation of the Post-Newtonian Approximation
2.1 Newtonian limit along a regular asymptotic Newtonian sequence
2.2 Post-Newtonian hierarchy
2.3 Explicit calculation in harmonic coordinates
3 Post-Newtonian Equations of Motion for Compact Binaries
3.1 Strong field point particle limit
3.2 Surface integral approach and body zone
3.3 Scalings on the initial hypersurface
3.4 Newtonian equations of motion for extended bodies
4 Formulation
4.1 Field equations
4.2 Near zone contribution
4.3 Lorentz contraction and multipole moments
4.4 General form of the equations of motion
4.5 On the arbitrary constant RA
4.6 Newtonian equations of motion
4.7 First post-Newtonian equations of motion
4.8 Body zone boundary dependent terms
5 Third Post-Newtonian Gravitational Field
5.1 Super-potential method
5.2 Super-potential-in-series method
5.3 Direct-integration method
6 Third Post-Newtonian Mass-Energy Relation
6.1 Meaning of PτAΘ
7 Third Post-Newtonian Momentum-Velocity Relation
8 Third Post-Newtonian Equations of Motion
8.1 Third post-Newtonian equations of motion with logarithmic terms
8.2 Arbitrary constant εRA
8.3 Consistency relation
8.4 Third post-Newtonian equations of motion
8.5 Comparison
8.6 Summary
8.7 Going further
9 Acknowledgements
A Far Zone Contribution
B Effects of Extendedness of Stars
B.1 Spin-orbit coupling force
B.2 Spin-spin coupling force
B.3 Quadrupole-orbit coupling force
B.4 Spin geodesic precession
B.5 Remarks
C A Generalized Equivalence Principle Including The Emission of Gravitational Wave
C.1 Introduction
C.2 Equations of motion
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