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E-raamat: Equations of Motion in General Relativity [Oxford Scholarship Online e-raamatud]

(Faculty of Science and Technology, Hirosaki University, Hirosaki, Japan), (Institute of Astronomy, Tohoku University, Sendai, Japan), (School of Physics, University College Dublin, Ireland)
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Equations of Motion in General RelativitySuurem pilt
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Wiley OnlineRohkem infot Oxford Scholarship Online e-raamatute kohta
Raamatu kodulehekülg: http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199584109.001.0001/acprof-9780199584109
The problem of motion of extended bodies in General Relativity is notorious for its analytical difficulty, but at the same time highly relevant for comparison of theoretical predictions with modern precision measurements in relativistic astrophysics and cosmology. Its one of the most important topics in General Relativity and its application to astrophysics.Equations of Motion in General Relativity focuses attention on two aspects of equations of motion in general relativity: the motion of extended bodies (stars) and the motion of small black holes. The objective is to offer a guide to prospective researchers into these areas of general relativity and to point out open questions and topics that are ripe for further development. It is over forty years since a text on this subject was published and in that time the research area of equations of motion in general relativity has undergone extraordinary development, stimulated by the discovery of the binary neutron star PSR 1913+16 in 1974 (which was the first isolated gravitating system found in which general relativity plays a fundamental role in describing theoretically its evolution), and more recently by the advent of kilometre size interferometric gravitational wave detectors which are expected to detect gravitational waves produced by coalescing binary neutron stars.
1 Introduction
1(4)
1.1 Equations of motion of extended bodies
1(1)
1.2 Equations of motion of small black holes
2(3)
2 Foundations of the post-Newtonian approximation
5(30)
2.1 Setting the scene
5(1)
2.2 Newtonian limit and asymptotic Newtonian sequence
6(2)
2.3 Post-Newtonian hierarchy
8(2)
2.4 A calculation using harmonic coordinates
10(3)
2.5 The strong field point particle limit
13(2)
2.6 Surface integrals and body zone
15(1)
2.7 Scalings on the initial hypersurface
16(1)
2.8 Newtonian equations for extended bodies
17(2)
2.9 Einstein's field equations
19(2)
2.10 Near zone and body zone contributions
21(5)
2.11 Lorentz contraction and multipole moments
26(1)
2.12 General form of the equations of motion
27(1)
2.13 Remarks on the arbitrary constant RA
28(1)
2.14 The Newtonian and 1PN equations of motion
29(4)
2.15 A comment on body zone boundary dependent terms
33(2)
3 The third post-Newtonian approximation
35(20)
3.1 Super-potential versus surface integrals
35(3)
3.2 3PN mass-energy relation
38(2)
3.3 The meaning of PτAO
40(1)
3.4 3PN momentum-velocity relation
41(2)
3.5 3PN equations of motion with log terms
43(1)
3.6 The arbitrary constant εRA
44(2)
3.7 Final form of 3PN equations of motion
46(6)
3.8 Observations and comments
52(3)
4 Two-body problem in general relativity
55(26)
4.1 Equations of motion for a binary system
55(1)
4.2 Periastron advance
56(6)
4.3 Light-like signals: Shapiro time delay
62(3)
4.4 Orbital period decay via gravitational radiation
65(2)
4.5 Perturbations of contact elements
67(4)
4.6 Perturbations of osculating elements
71(1)
4.7 Perturbations due to gravitational radiation reaction
72(2)
4.8 Derivations by balance arguments
74(4)
4.9 Spin effects
78(3)
5 Small black holes: geometrical preliminaries
81(12)
5.1 The Fermi property of the background
81(5)
5.2 The line-element of the background
86(2)
5.3 The field equations near r = 0
88(5)
6 Small charged black holes: equations of motion
93(14)
6.1 Black hole as perturbation of background
93(2)
6.2 The vacuum Einstein-Maxwell field equations
95(7)
6.3 The equations of motion
102(2)
6.4 Observations and prospects
104(3)
7 Gravitational physics of few-body systems
107(12)
7.1 Choreographic solutions for the N-body problem
107(2)
7.2 Gravitational waves from few-body systems
109(3)
7.3 General relativistic figure-eight solution
112(7)
Appendix A Far zone contribution 119(6)
Appendix B Effects of extendedness of stars 125(8)
Appendix C Null geodesic congruences 133(4)
Appendix D Perturbed field equations 137(6)
References 143(8)
Index 151
Hideki Asada [ Research Fellow, previously: Yukawa Institute for Theoretical Physics, Kyoto University; Institut d'Astrophysique de Paris]

Toshifumi Futamase [ Research Fellow, previously: Max Planck Institute, Munich; Washington University, St. Louis; University College Cardiff]

Peter Hogan [ Research Fellow, previously: School of Theoretical Physics, Dublin Institute for Advanced Studies; University of Texas, Austin; Trinity College, Dublin]
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