The motion of point particles in curved spacetime

Living Reviews in Relativity

Volumn 14, Issue , 2011, Pages

  Poisson, Eric ^a   Pound, Adam ^a   Vega, Ian ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80755142840     PISSN: None     EISSN: 14338351     Source Type: Journal    
DOI: 10.12942/lrr-2011-7     Document Type: Review

References (187)

1. S., "Fast frequency-domain algorithm for gravitational self-force: Circular orbits in Schwarzschild spacetime", Phys. Rev. D, 83, 124026, (2011). [DOI], [arXiv:1012.5860].
2. K., "Approximate binary-black-hole metric", Phys. Rev. D, 61, 124013, 1-19, (2000). [DOI], [arXiv:gr-qc/9912113].
3. Anderson, P.R., Eftekharzadeh, A. and Hu, B.L., "Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion", Phys. Rev. D, 73, 064023, (2006). [DOI], [arXiv:gr-qc/0507067].
4. Anderson, P.R. and Hu, B.L., "Radiation reaction in Schwarzschild spacetime: Retarded Green's function via Hadamard-WKB expansion", Phys. Rev. D, 69, 064039, (2004). [DOI], [arXiv:gr-qc/0308034].
5. Anderson, W.G., Flanagan, ÉÉ and Ottewill, A.C., "Quasilocal contribution to the gravitational self-force", Phys. Rev. D, 71, 024036, (2005). [DOI], [arXiv:gr-qc/0412009].
6. Anderson, W.G. and Wiseman, A.G., "A matched expansion approach to practical self-force calculations", Class. Quantum Grav., 22, S783-S800, (2005). [DOI], [arXiv:gr-qc/0506136].
7. L., "Self-force on a scalar particle in spherically symmetric spacetime via mode-sum regularization: Radial trajectories", Phys. Rev. D, 62, 084027, 1-21, (2000). [DOI], [arXiv:grqc/0005042].
8. L., "Gravitational self-force by mode sum regularization", Phys. Rev. D, 64, 084021, 1-16, (2001). [DOI], [arXiv:gr-qc/0105040].
9. L., "Gravitational self-force in extreme mass-ratio inspirals", Class. Quantum Grav., 26, 213001, (2009). [DOI], [arXiv:0902.0573].
10. Barack, L. and Burko, L.M., "Radiation-reaction force on a particle plunging into a black hole", Phys. Rev. D, 62, 084040, 1-5, (2000). [DOI], [arXiv:gr-qc/0007033].
11. Barack, L., Damour, T. and Sago, N., "Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism", Phys. Rev. D, 82, 084036, (2010). [DOI], [arXiv:1008.0935].
12. Barack, L. and Golbourn, D.A., "Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions", Phys. Rev. D, 76, 044020, (2007). [DOI], [arXiv:0705.3620].
13. Barack, L., Golbourn, D.A. and Sago, N., "M-mode regularization scheme for the self-force in Kerr spacetime", Phys. Rev. D, 76, 124036, (2007). [DOI], [arXiv:0709.4588].
14. Barack, L. and Lousto, C.O., "Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole", Phys. Rev. D, 66, 061502, 1-5, (2002). [DOI], [arXiv:gr-qc/0205043].
15. Barack, L., Mino, Y., Nakano, H., Ori, A. and Sasaki, M., "Calculating the Gravitational Self-Force in Schwarzschild Spacetime", Phys. Rev. Lett., 88, 091101, 1-4, (2002). [DOI], [arXiv:gr-qc/0111001].
16. Barack, L. and Ori, A., "Mode sum regularization approach for the self-force in black hole spacetime", Phys. Rev. D, 61, 061502, 1-5, (2000). [DOI], [arXiv:gr-qc/9912010].
17. Barack, L. and Ori, A., "Gravitational self-force and gauge transformations", Phys. Rev. D, 64, 124003, 1-13, (2001). [DOI], [arXiv:gr-qc/0107056].
18. Barack, L. and Ori, A., "Regularization parameters for the self-force in Schwarzschild spacetime: Scalar case", Phys. Rev. D, 66, 084022, 1-15, (2002). [DOI], [arXiv:gr-qc/0204093].
19. Barack, L. and Ori, A., "Gravitational Self-Force on a Particle Orbiting a Kerr Black Hole", Phys. Rev. Lett., 90, 111101, 1-4, (2003). [DOI], [arXiv:gr-qc/0212103].
20. Barack, L. and Ori, A., "Regularization parameters for the self-force in Schwarzschild spacetime. II. Gravitational and electromagnetic cases", Phys. Rev. D, 67, 024029, 1-11, (2003). [DOI], [arXiv:gr-qc/0209072].
21. Barack, L. and Sago, N., "Gravitational self-force on a particle in circular orbit around a Schwarzschild black hole", Phys. Rev. D, 75, 064021, (2007). [DOI], [arXiv:gr-qc/0701069].
22. Barack, L. and Sago, N., "Gravitational Self-Force Correction to the Innermost Stable Circular Orbit of a Schwarzschild Black Hole", Phys. Rev. Lett., 102, 191101, (2009). [DOI], [arXiv:0902.0573].
23. Barack, L. and Sago, N., "Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole", Phys. Rev. D, 81, 084021, (2010). [DOI], [arXiv:1002.2386].
24. Barack, L. and Sago, N., "Beyond the geodesic approximation: Conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole", Phys. Rev. D, 83, 084023, (2011). [DOI], [arXiv:1101.3331].
25. Barton, J.L., Lazar, D., Kennefick, D.J., Khanna, G. and Burko, L.M., "Computational efficiency of frequency- and time-domain calculations of extreme mass-ratio binaries: Equatorial orbits", Phys. Rev. D, 78, 064042, (2010). [arXiv:0804.1075].
26. [Blanchet, L., "Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries", Living Rev. Relativity, 9, lrr-2006-4, (2006). [arXiv:gr-qc/0202016]. URL (accessed 25 August 2010): http://www.livingreviews.org/lrr-2006-4.
27. Blanchet, L. and Damour, T., "Radiative gravitational fields in general relativity I. General structure of the field outside the source", Philos. Trans. R. Soc. London, Ser. A, 320, 379-430, (1986).
28. Blanchet, L., Detweiler, S., Le Tiec, A. and Whiting, B.F., "High-order post-Newtonian fit of the gravitational self-force for circular orbits in the Schwarzschild geometry", Phys. Rev. D, 81, 084033, (2010). [arXiv:1002.0726].
29. Blanchet, L., Detweiler, S., Le Tiec, A. and Whiting, B.F., "Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry", Phys. Rev. D, 81, 064004, (2010). [arXiv:0910.0207].
30. L.M., "Self-Force on a Particle in Orbit around a Black Hole", Phys. Rev. Lett., 84, 4529-4532, (2000). [DOI], [arXiv:gr-qc/0003074].
31. L.M., "Self-force on static charges in Schwarzschild spacetime", Class. Quantum Grav., 17, 227-250, (2000). [DOI], [arXiv:gr-qc/9911042].
32. L.M., "The importance of conservative self forces for binaries undergoing radiation damping", Int. J. Mod. Phys. A, 16, 1471-1479, (2001). [DOI].
33. Burko, L.M., Harte, A.I. and Poisson, E., "Mass loss by a scalar charge in an expanding universe", Phys. Rev. D, 65, 124006, 1-11, (2002). [DOI], [arXiv:gr-qc/0201020].
34. Burko, L. and Khanna, G., "Accurate time-domain gravitational waveforms for extrememass- ratio binaries", Europhys. Lett., 78, 60005, (2007). [DOI], [arXiv:gr-qc/0609002].
35. Burko, L.M. and Liu, Y.T., "Self-force on a scalar charge in the spacetime of a stationary, axisymmetric black hole", Phys. Rev. D, 64, 024006, 1-21, (2001). [DOI], [arXiv:gr-qc/0103008].
36. [Burko, L.M., Liu, Y.T. and Soen, Y., "Self-force on charges in the spacetime of spherical shells", Phys. Rev. D, 63, 024015, 1-18, (2001). [arXiv:gr-qc/0008065].
37. [Canizares, P. and Sopuerta, C.F., "Efficient pseudospectral method for the computation of the self-force on a charged particle: Circular geodesics around a Schwarzschild black hole", Phys. Rev. D, 79, 084020, (2009). [arXiv:0903.0505].
38. Canizares, P., Sopuerta, C.F. and Jaramillo, J.L., "Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole", Phys. Rev. D, 82, 044023, (2010). [DOI], [arXiv:1006.3201].
39. Casals, M., Dolan, S., Ottewill, A.C. and Wardell, B., "Pad/e approximants of the Green function in spherically symmetric spacetimes", Phys. Rev. D, 79, 124044, (2009). [DOI], [arXiv:0903.5319].
40. Casals, M., Dolan, S., Ottewill, A.C. and Wardell, B., "Self-force calculations with matched expansions and quasinormal mode sums", Phys. Rev. D, 79, 124043, (2009). [DOI], [arXiv:0903.0395].
41. P.L., "Vector potential and metric perturbations of a rotating black hole", Phys. Rev. D, 11, 2042-2062, (1975). [DOI].
42. Cohen, J.M. and Kegeles, L.S., "Electromagnetic fields in curved spaces: a constructive procedure", Phys. Rev. D, 10, 1070-1084, (1974). [DOI].
43. E.T., "On Electrostatics in a Gravitational Field", Proc. R. Soc. London, Ser. A, 116, 720-735, (1928).
44. T., "Gravitational self-force in a Schwarzschild background and the effective onebody formalism", Phys. Rev. D, 81, 024017, (2010). [DOI], [arXiv:0910.5533].
45. Damour, T. and Iyer, B.R., "Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors", Phys. Rev. D, 43, 3259-3272, (1991). [DOI].
46. P.D., "Dynamics of a small black hole in a background universe", Phys. Rev. D, 11, 1387-1403, (1975). [DOI].
47. D'Eath, P.D., Black Holes: Gravitational Interactions, (Clarendon Press; Oxford University Press, Oxford; New York, 1996).
48. Décanini, Y. and Folacci, A., "Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator", Phys. Rev. D, 73, 044027, 1-38, (2006). [DOI], [arXiv:gr-qc/0511115].
49. S., "Perspective on gravitational self-force analyses", Class. Quantum Grav., 22, 681-716, (2005). [DOI], [arXiv:gr-qc/0501004].
50. S., "Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry", Phys. Rev. D, 77, 124026, (2008). [DOI], [arXiv:gr-qc/0410011].
51. Detweiler, S., Messaritaki, E. and Whiting, B.F., "Self-force of a scalar field for circular orbits about a Schwarzschild black hole", Phys. Rev. D, 67, 104016, (2003). [DOI], [arXiv:grqc/0205079].
52. Detweiler, S. and Poisson, E., "Low multipole contributions to the gravitational self-force", Phys. Rev. D, 69, 084019, (2004). [DOI], [arXiv:gr-qc/0312010].
53. Detweiler, S. and Whiting, B.F., "Self-force via a Green's function decomposition", Phys. Rev. D, 67, 024025, (2003). [DOI], [arXiv:gr-qc/0202086].
54. DeWitt, B.S. and Brehme, R.W., "Radiation Damping in a Gravitational Field", Ann. Phys. (N.Y.), 9, 220-259, (1960). [DOI].
55. Diaz-Rivera, L.M., Messaritaki, E., Whiting, B.F. and Detweiler, S., "Scalar field self-force effects on orbits about a Schwarzschild black hole, eccentric orbits", Phys. Rev. D, 70, 124018, (2004). [DOI], [arXiv:gr-qc/0410011].
56. P.A.M., "Classical theory of radiating electrons", Proc. R. Soc. London, Ser. A, 167, 148, (1938).
57. W.G., "Dynamics of extended bodies in general relativity. I. Momentum and angular momentum", Proc. R. Soc. London, Ser. A, 314, 499-527, (1970).
58. W.G., "Dynamics of extended bodies in general relativity. II. Moments of the chargecurrent vector", Proc. R. Soc. London, Ser. A, 319, 509-547, (1970).
59. W.G., "Dynamics of Extended Bodies in General Relativity. III. Equations of Motion", Philos. Trans. R. Soc. London, Ser. A, 277, 59-119, (1974).
60. Dolan, S. and Barack, L., "Self-force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild spacetime", Phys. Rev. D, 83, 124019, (2011). [DOI], [arXiv:1010.5255].
61. Drasco, S., Flanagan, É É and Hughes, S.A., "Computing inspirals in Kerr in the adiabatic regime: I. The scalar case", Class. Quantum Grav., 22, S801-S846, (2005). [DOI], [arXiv:grqc/0505075].
62. Drasco, S. and Hughes, S.A., "Gravitational wave snapshots of generic extreme mass ratio inspirals", Phys. Rev. D, 73, 024027, (2006). [DOI], [arXiv:gr-qc/0509101].
63. [Eckhaus, W., Asymptotic Analysis of Singular Perturbations, Studies in Mathematics and its Applications, 9, (North-Holland, Amsterdam; New York, 1979). [Google Books].
64. Ehlers, J. and Geroch, R., "Equation of motion of small bodies in relativity", Ann. Phys. (N.Y.), 309, 232-236, (2004). [DOI], [arXiv:gr-qc/0309074].
65. Ehlers, J. and Rudolph, E., "Dynamics of extended bodies in general relativity center-ofmass description and quasirigidity", Gen. Relativ. Gravit., 8, 197-217, (1977). [DOI].
66. Einstein, A. and Infeld, L., "On the motion of particles in general relativity theory", Can. J. Math., 1, 209, (1949). [DOI].
67. Field, S.E., Hesthaven, J.S. and Lau, S.R., "Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries", Class. Quantum Grav., 26, 165010, (2009). [DOI], [arXiv:0902.1287].
68. Field, S.E., Hesthaven, J.S. and Lau, S.R., "Persistent junk solutions in time-domain modeling of extreme mass ratio binaries", Phys. Rev. D, 81, 124030, (2010). [DOI], [arXiv:1001.2578].
69. Flanagan, ÉÉ and Hinderer, T., "Transient resonances in the inspirals of point particles into black holes", arXiv, e-print, (2010). [arXiv:1009.4923 [gr-qc]].
70. Flanagan, ÉÉ and Wald, R.M., "Does back reaction enforce the averaged null energy condition in semiclassical gravity?", Phys. Rev. D, 54, 6233-6283, (1996). [DOI], [arXiv:grqc/9602052].
71. Friedlander, F.G., The wave equation on a curved space-time, Cambridge Monographs on Mathematical Physics, 2, (Cambridge University Press, Cambridge; New York, 1975).[Google Books].
72. Fukumoto, T., Futamase, T. and Itoh, Y., "On the equation of motion for a fast moving small object using the strong field point particle limit", Prog. Theor. Phys., 116, 423-428, (2006). [DOI], [arXiv:gr-qc/0606114].
73. Futamase, T., Hogan, P.A. and Itoh, Y., "Equations of Motion in General Relativity of a Small Charged Black Hole", Phys. Rev. D, 78, 104014, (2008). [arXiv:0811.4020].
74. Futamase, T. and Itoh, Y., "The Post-Newtonian Approximation for Relativistic Compact Binaries", Living Rev. Relativity, 10, lrr-2007-2, (2007). URL (accessed 25 August 2010): http://www.livingreviews.org/lrr-2007-2.
75. Galley, C.R. and Hu, B.L., "Self-force on extreme mass ratio inspirals via curved spacetime effective field theory", Phys. Rev. D, 79, 064002, (2009). [DOI], [arXiv:0801.0900].
76. Galley, C.R., Hu, B.L. and Lin, S.-Y., "Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space", Phys. Rev. D, 74, 024017, (2006).[DOI], [arXiv:gr-qc/0603099].
77. D.V., "Radiation reaction in the Kerr gravitational field", J. Phys. A: Math. Gen., 15, 3737-3749, (1982). [DOI].
78. Ganz, K., Hikida, W., Nakano, H., Sago, N. and Tanaka, T., "Adiabatic evolution of three 'constants' of motion for greatly inclined orbits in Kerr spacetime", Prog. Theor. Phys., 117, 1041-1066, (2007). [DOI], [arXiv:gr-qc/0702054].
79. Geroch, R. and Jang, P.S., "Motion of a body in general relativity", J. Math. Phys., 16, 65-67, (1975). [DOI].
80. Geroch, R. and Traschen, J., "Strings and other distributional sources in general relativity", Phys. Rev. D, 36, 1017-1031, (1987). [DOI].
81. S.E., "Comments on First and Second Order Gravitational Self-Force", Presentation at the 12th Capra Meeting on Radiation Reaction, conference paper, (2009).
82. Gralla, S.E., Harte, A.I. and Wald, R.M., "A Rigorous Derivation of Electromagnetic Selfforce", Phys. Rev. D, 80, 024031, (2009). [DOI], [arXiv:0905.2391].
83. Gralla, S.E. and Wald, R.M., "A Rigorous Derivation of Gravitational Self-force", Class. Quantum Grav., 25, 205009, (2008). [DOI], [arXiv:0806.3293].
84. R., "Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation", Phys. Rev. D, 75, 124011, (2007). [DOI], [arXiv:0704.0797].
85. Haas, R., Self-force on point particles in orbit around a Schwarzschild black hole, Ph.D. Thesis, (University of Guelph, Guelph, 2008). [ADS].
86. Haas, R. and Poisson, E., "Mass change and motion of a scalar charge in cosmological spacetimes", Class. Quantum Grav., 22, S739-S752, (2005). [DOI], [arXiv:gr-qc/0411108].
87. Haas, R. and Poisson, E., "Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field", Phys. Rev. D, 74, 004009, (2006). [DOI], [arXiv:gr-qc/0605077].
88. Hadamard, J., Lectures on Cauchy's Problem in Linear Partial Differential Equations, (Yale University Press, New Haven, CT, 1923). [Google Books]. Online version (accessed 3 February 2011): http://www.archive.org/details/lecturesoncauchy00hadauoft.
89. A.I., "Self-forces from generalized Killing fields", Class. Quantum Grav., 25, 235020, (2008). [DOI], [arXiv:0807.1150].
90. A.I., "Electromagnetic self-forces and generalized Killing fields", Class. Quantum Grav., 26, 155015, (2009). [DOI], [arXiv:0903.0167].
91. A.I., "Effective stress-energy tensors, self-force, and broken symmetry", Class. Quantum Grav., 27, 135002, (2010). [DOI], [arXiv:0910.4614].
92. P., "Radiation Damping in General Relativity", Phys. Rev., 108(5), 1351-1352, (1957). [DOI].
93. Havas, P. and Goldberg, J.N., "Lorentz-Invariant Equations of Motion of Point Masses in the General Theory of Relativity", Phys. Rev., 128(1), 398-414, (1962). [DOI].
94. Hinderer, T. and Flanagan, ÉÉ, "Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion", Phys. Rev. D, 78, 064028, (2008). [DOI], [arXiv:0805.3337].
95. J.M., "A Vierbein Formalism for Radiation Damping", Ann. Phys. (N.Y.), 47, 141-165, (1968).
96. Holmes, M.H., Introduction to Perturbation Methods, Texts in Applied Mathematics, 20, (Springer, Berlin; New York, 1995). [Google Books].
97. Huerta, E.A. and Gair, J.R., "Influence of conservative corrections on parameter estimation for EMRIs", Phys. Rev. D, 79, 084021, (2009). [DOI], [arXiv:0812.4208].
98. S., "Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational-wave emission", Phys. Rev. D, 61, 084004, (2000). [DOI], [arXiv:gr-qc/9910091].
99. Hughes, S., Drasco, S., Flanagan, ÉÉ and Franklin, J., "Gravitational radiation reaction and inspiral waveforms in the adiabatic limit", Phys. Rev. Lett., 94, 221101, (2005). [DOI],[arXiv:gr-qc/0504015].
100. Infeld, L. and Schild, A., "On the Motion of Test Particles in General Relativity", Rev. Mod. Phys., 21, 408-413, (1949). [DOI].
101. Jackson, J.D., Classical Electrodynamics, (Wiley, New York, 1999), 3rd edition.
102. R.E., "Motion of a small body through an external field in general relativity calculated by matched asymptotic expansions", Phys. Rev. D, 22, 1853-1870, (1980). [DOI].
103. R.E., "Motion of an electrically or magnetically charged body with possibly strong internal gravity through external electromagnetic and gravitational fields", Phys. Rev. D, 22, 1879-1881, (1980). [DOI].
104. R.E., "Underlying structure of singular perturbations on manifolds", Ann. Phys. (N.Y.), 132, 1-17, (1981). [DOI].
105. Kegeles, L.S. and Cohen, J.M., "Constructive procedure for perturbations of spacetimes", Phys. Rev. D, 19, 1641-1664, (1979). [DOI].
106. Keidl, T., Self-force for extreme mass ratio inspiral, Ph.D. Thesis, (University of Wisconsin- Milwaukee, Milwaukee, 2008). [ADS].
107. Keidl, T.S., Friedman, J.L. and Wiseman, A.G., "Finding fields and self-force in a gauge appropriate to separable wave equations", Phys. Rev. D, 75, 124009, (2006). [arXiv:grqc/0611072].
108. Keidl, T.S., Shah, A.G., Friedman, J.L., Kim, D.H. and Price, L.R., "Gravitational self-force in a radiation gauge", Phys. Rev. D, 82, 124012, (2010). [DOI], [arXiv:1004.2276].
109. Kevorkian, J. and Cole, J.D., Multiple Scale and Singular Perturbation Methods, Applied Mathematical Sciences, 114, (Springer, New York, 1996). [Google Books].
110. Khanna, G., "Teukolsky evolution of particle orbits around Kerr black holes in the time domain: Elliptic and inclined orbits", Phys. Rev. D, 69, 024016, (2006). [arXiv:gr-qc/0309107].
111. Lagerstrom, P.A., Matched Asymptotic Expansions: Ideas and Techniques, Applied Mathematical Sciences, 76, (Springer, New York, 1988).
112. Landau, L.D. and Lifshitz, E.M., The Classical Theory of Fields, Course of Theoretical Physics, 2, (Pergamon Press, Oxford; New York, 1975), 4th edition. [Google Books].
113. Leaute, B. and Linet, B., "Electrostatics in a Reissner-Nordstr̈om space-time", Phys. Lett. A, 58, 5-6, (1976). [DOI].
114. B., "Electrostatics and magnetostatics in Schwarzschild metric", J. Phys. A: Math. Gen., 9, 1081-1087, (1976). [DOI].
115. "LISA Home Page (NASA)", project homepage, Jet Propulsion Laboratory/NASA. URL (accessed 2 April 2004): http://lisa.jpl.nasa.gov/.
116. Lopez-Aleman, R., Khanna, G. and Pullin, J., "Perturbative evolution of particle orbits around Kerr black holes: time domain calculation", Class. Quantum Grav., 20, 3259-3268, (2003). [DOI], [arXiv:gr-qc/0303054].
117. C.O., "Pragmatic Approach to Gravitational Radiation Reaction in Binary Black Holes", Phys. Rev. Lett., 84, 5251-5254, (2000). [DOI], [arXiv:gr-qc/9912017].
118. Lousto, C.O., ed., Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach, Class. Quantum Grav., 22, (IOP Publishing, Bristol, 2005).
119. Lousto, C.O. and Nakano, H., "A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources", Class. Quantum Grav., 25, 145018, (2008). [DOI],[arXiv:0802.4277].
120. Lousto, C.O. and Price, R.H., "Understanding initial data for black hole collisions", Phys. Rev. D, 56, 6439-6457, (1997). [DOI], [arXiv:gr-qc/9705071].
121. Lousto, C.O. and Whiting, B.F., "Reconstruction of black hole metric perturbations from the Weyl curvature", Phys. Rev. D, 66, 024026, 1-7, (2002). [DOI], [arXiv:gr-qc/0203061].
122. Manasse, F.K. and Misner, C.W., "Fermi normal coordinates and some basic concepts in differential geometry", J. Math. Phys., 4, 735-745, (1963). [DOI].
123. Martel, K. and Poisson, E., "One-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole", Phys. Rev. D, 66, 084001, (2002).[DOI], [arXiv:gr-qc/0107104].
124. Y., "Perturbative approach to an orbital evolution around a supermassive black hole", Phys. Rev. D, 67, 084027, 1-17, (2003). [DOI], [arXiv:gr-qc/0302075].
125. Mino, Y., "Self-force in the radiation reaction formula - adiabatic approximation of a metric perturbation and an orbit", Prog. Theor. Phys., 113, 733-761, (2005). [arXiv:gr-qc/0506003].
126. Y., "Adiabatic expansion for a metric perturbation and the condition to solve the gauge problem for gravitational radiation reaction problem", Prog. Theor. Phys., 115, 43-61, (2006). [DOI], [arXiv:gr-qc/0601019].
127. Mino, Y., Nakano, H. and Sasaki, M., "Covariant Self-Force Regularization of a Particle Orbiting a Schwarzschild Black Hole - Mode Decomposition Regularization", Prog. Theor. Phys., 108, 1039-1064, (2003). [arXiv:gr-qc/0111074].
128. Mino, Y. and Price, R., "Two-timescale adiabatic expansion of a scalar field model", Phys. Rev. D, 77, 064001, (2008). [DOI], [arXiv:0801.0179].
129. Mino, Y., Sasaki, M. and Tanaka, T., "Gravitational radiation reaction", Prog. Theor. Phys. Suppl., 128, 373-406, (1997). [DOI], [arXiv:gr-qc/9712056].
130. Mino, Y., Sasaki, M. and Tanaka, T., "Gravitational radiation reaction to a particle motion", Phys. Rev. D, 55, 3457-3476, (1997). [DOI], [arXiv:gr-qc/9606018].
131. Misner, C.W., Thorne, K.S. and Wheeler, J.A., Gravitation, (W.H. Freeman, San Francisco, 1973).
132. Morette-DeWitt, C. and DeWitt, B.S., "Falling charges", Physics, 1, 3-20, (1964).
133. Morette-DeWitt, C. and Ging, J.L., "Freinage dû à la radiation gravitationnelle", C. R. Hebd. Seanc. Acad. Sci., 251, 1868, (1960).
134. A., "Reconstruction of inhomogeneous metric perturbations and electromagnetic fourpotential in Kerr spacetime", Phys. Rev. D, 67, 124010, 1-19, (2003). [DOI], [arXiv:grqc/0207045].
135. Ori, A. and Thorne, K.S., "Transition from inspiral to plunge for a compact body in a circular equatorial orbit around a massive, spinning black hole", Phys. Rev. D, 62, 124022, (2000).[DOI], [arXiv:gr-qc/0003032].
136. Ottewill, A.C. and Wardell, B., "Quasilocal contribution to the scalar self-force: Geodesic motion", Phys. Rev. D, 77, 104002, (2008). [DOI], [arXiv:0711.2469].
137. Ottewill, A.C. and Wardell, B., "Quasilocal contribution to the scalar self-force: Nongeodesic motion", Phys. Rev. D, 79, 024031, (2009). [DOI], [arXiv:0810.1961].
138. A., "Spinning Test-Particles in General Relativity. I", Proc. R. Soc. London, Ser. A, 209, 248-258, (1951). [DOI], [ADS].
139. P.C., "Gravitational radiation and the motion of two point masses", Phys. Rev., 136, B1224-B1232, (1964). [DOI].
140. Peters, P.C. and Mathews, J., "Gravitational radiation from point masses in a Keplerian orbit", Phys. Rev., 131, 435-440, (1963). [DOI].
141. Pfenning, M.J. and Poisson, E., "Scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes", Phys. Rev. D, 65, 084001, 1-30, (2002). [DOI], [arXiv:grqc/0012057].
142. E., "Retarded coordinates based at a world line and the motion of a small black hole in an external universe", Phys. Rev. D, 69, 084007, (2004). [DOI], [arXiv:gr-qc/0311026].
143. Pound, A., Motion of small bodies in general relativity: foundations and implementations of the self-force, Ph.D. Thesis, (University of Guelph, Guelph, 2010). [arXiv:1006.3903].
144. A., "Self-consistent gravitational self-force", Phys. Rev. D, 81, 024023, (2010). [DOI],[arXiv:0907.5197].
145. A., "Singular perturbation techniques in the gravitational self-force problem", Phys. Rev. D, 81, 124009, (2010). [DOI], [arXiv:1003.3954].
146. Pound, A. and Poisson, E., "Multi-scale analysis of the electromagnetic self-force in a weak gravitational field", Phys. Rev. D, 77, 044012, (2008). [DOI], [arXiv:0708.3037].
147. Pound, A. and Poisson, E., "Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals", Phys. Rev. D, 77, 044013, (2008). [DOI],[arXiv:0708.3033].
148. Pound, A., Poisson, E. and Nickel, B.G., "Limitations of the adiabatic approximation to the gravitational self-force", Phys. Rev. D, 72, 124001, (2005). [DOI], [arXiv:gr-qc/0509122].
149. T.C., "Axiomatic approach to radiation reaction of scalar point particles in curved spacetime", Phys. Rev. D, 62, 064029, 1-9, (2000). [DOI], [arXiv:gr-qc/0005030].
150. Quinn, T.C. and Wald, R.M., "An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime", Phys. Rev. D, 56, 3381-3394, (1997).[DOI], [arXiv:gr-qc/9610053].
151. Quinn, T.C. and Wald, R.M., "Energy conservation for point particles undergoing radiation reaction", Phys. Rev. D, 60, 064009, 1-20, (1999). [DOI], [arXiv:gr-qc/9903014].
152. Racine, E. and Flanagan, ÉÉ, "Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies", Phys. Rev. D, 71, 044010, (2005). [DOI], [arXiv:gr-qc/0404101].
153. Roach, G.F., Green's Functions, (Cambridge University Press, Cambridge; New York, 1982), 2nd edition. [Google Books].
154. Rohrlich, F., Classical Charged Particles, (World Scientific, Singapore; Hackensack, NJ, 2007), 3rd edition. [Google Books].
155. E., "Construction of the second-order gravitational perturbations produced by a compact object", Phys. Rev. D, 73, 044034, (2006). [DOI], [arXiv:gr-qc/0602066].
156. Rosenthal, E., "Second-order gravitational self-force", Phys. Rev. D, 74, 084018, (2006).[DOI], [arXiv:gr-qc/0609069].
157. Sago, N., Barack, L. and Detweiler, S., "Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results", Phys. Rev. D, 78, 124024, (2008).[DOI], [arXiv:0810.2530].
158. Sago, N., Tanaka, T., Hikida, W., Ganz, K. and Nakano, H., "Adiabatic evolution of orbital parameters in the Kerr spacetime", Prog. Theor. Phys., 115, 873-907, (2006). [DOI], [arXiv:grqc/0511151].
159. Sago, N., Tanaka, T., Hikida, W. and Nakano, H., "Adiabatic radiation reaction to orbits in Kerr spacetime", Prog. Theor. Phys., 114, 509-514, (2005). [DOI], [arXiv:gr-qc/0506092].
160. R., "The center of mass in general relativity", Gen. Relativ. Gravit., 10, 377-393, (1979).
161. Sciama, D.W., Waylen, P.C. and Gilman, R.C., "Generally Covariant Integral Formulation of Einstein's Field Equations", Phys. Rev., 187, 1762-1766, (1969). [DOI].
162. Shankar, K. and Whiting, B.F., "Self-force of a static electric charge near a Schwarzschild star", Phys. Rev. D, 76, 124027, (2007). [DOI], [arXiv:0707.0042].
163. Smith, A.G. and Will, C.M., "Force on a static charge outside a Schwarzschild black hole", Phys. Rev. D, 22, 1276-1284, (1980). [DOI].
164. Steinbauer, R. and Vickers, J.A., "The use of Generalised Functions and Distributions in General Relativity", Class. Quantum Grav., 23, R91-R114, (2006). [DOI], [arXiv:gr-qc/0603078].
165. Steinhoff, J. and Puetzfeld, D., "Multipolar equations of motion for extended test bodies in General Relativity", Phys. Rev. D, 81, 044019, (2010). [DOI], [arXiv:0909.3756].
166. J.M., "Hertz-Bromwich-Debye-Whittaker-Penrose potentials in general relativity", Proc. R. Soc. London, Ser. A, 367, 527-538, (1979).
167. P., "Transition from adiabatic inspiral to geodesic plunge for a compact object around a massive Kerr black hole: Generic orbits", Phys. Rev. D, 77, 124050, (2008). [DOI],[arXiv:0803.4482].
168. Sundararajan, P., Khanna, G. and Hughes, S.A., "Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation", Phys. Rev. D, 76, 104005, (2007). [DOI], [arXiv:gr-qc/0703028].
169. Synge, J.L., Relativity: The General Theory, (North-Holland, Amsterdam, 1960).
170. Taylor, S. and Poisson, E., "Nonrotating black hole in a post-Newtonian tidal environment", Phys. Rev. D, 78, 084016, (2008). [DOI], [arXiv:0806.3052].
171. Teitelboim, C., Villarroel, D. and van Weert, C.G., "Classical electrodynamics of retarded fields and point particles", Riv. Nuovo Cimento, 3, 9, (1980). [DOI].
172. S.A., "Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations", Astrophys. J., 185, 635-647, (1973). [DOI], [ADS].
173. K.S., "Multipole expansions of gravitational radiation", Rev. Mod. Phys., 52, 299-339, (1980). [DOI], [ADS].
174. Thorne, K.S. and Hartle, J.B., "Laws of motion and precession for black holes and other bodies", Phys. Rev. D, 31, 1815-1837, (1985). [DOI].
175. Vega, I., The dynamics of point particles around black holes, Ph.D. Thesis, (University of Florida, Gainesville, 2009).
176. Vega, I. and Detweiler, S., "Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application", Phys. Rev. D, 77, 084008, (2008). [DOI],[arXiv:0712.4405].
177. Vega, I., Diener, P., Tichy, W. and Detweiler, S., "Self-force with (3+1) codes: a primer for numerical relativists", Phys. Rev. D, 80, 084021, (2009). [DOI], [arXiv:0908.2138].
178. [Verhulst, F., Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Texts in Applied Mathematics, 50, (Springer, New York, 2005). [Google Books].
179. R.M., "Construction of Solutions of Gravitational, Electromagnetic, or Other Perturbation Equations from Solutions of Decoupled Equations", Phys. Rev. Lett., 41, 203-206, (1978). [DOI].
180. Walker, M. and Will, C.M., "The approximation of radiative effects in relativistic gravity - Gravitational radiation reaction and energy loss in nearly Newtonian systems", Astrophys. J. Lett., 242, L129-L133, (1980). [DOI].
181. Warburton, N. and Barack, L., "Self-force on a scalar charge in Kerr spacetime: Circular equatorial orbits", Phys. Rev. D, 81, 084039, (2010). [DOI], [arXiv:1003.1860].
182. Wardell, B., Green Functions and Radiation Reaction From a Spacetime Perspective, Ph.D. Thesis, (University College Dublin, Dublin, 2009). [arXiv:0910.2634].
183. B.F., "Identifying the singular field for self-force evaluation", Class. Quantum Grav., 22, S661-S679, (2005). [DOI].
184. Whiting, B.F. and Price, L.P., "Metric reconstruction from Weyl scalars", Class. Quantum Grav., 22, S589-S604, (2005). [DOI].
185. A.G., "Self-force on a static scalar test charge outside a Schwarzschild black hole", Phys. Rev. D, 61, 084014, 1-14, (2000). [DOI], [arXiv:gr-qc/0001025].
186. Zel'nikov, A.I and Frolov, V.P., "Influence of gravitation on the self-energy of charged particles", Sov. Phys. JETP, 55, 919-198, (1982).
187. X.-H., "Multipole expansions of the general-relativistic gravitational field of the external universe", Phys. Rev. D, 34, 991-1004, (1986). [DOI].