Characteristic evolution and matching

Living Reviews in Relativity

Volumn 8, Issue , 2005, Pages

  Winicour, Jeffrey ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28844433069     PISSN: 14338351     EISSN: 14338351     Source Type: Journal    
DOI: 10.12942/lrr-2005-10     Document Type: Review

References (229)

1. Abrahams, A.M., and Evans, C.R., "Gauge-invariant treatment of gravitational radiation near the source: Analysis and numerical simulations", Phys. Rev. D, 42(8), 2585-2594, (1990). 1, 4.8
2. Abrahams, A.M., and Price, R.H., "Applying black hole perturbation theory to numerically generated spacetimes", Phys. Rev. D, 53(4), 1963-1971, (1996). 1, 4.3
3. Abrahams, A.M., Rezzolla, L., Rupright, M.E., Anderson, A., Anninos, P., Baumgarte, T.W., Bishop, N.T., Brandt, S.R., Browne, J.C., Camarda, K., Choptuik, M.W., Cook, G.B., Correll, R.R., Evans, C.R., Finn, L.S., Fox, G.C., Gómez, R., Haupt, T., Huq, M.F., Kidder, L.E., Klasky, S.A., Laguna, P., Landry, W., Lehner, L., Lenaghan, J., Marsa, R.L., Massó, J., Matzner, R.A., Mitra, S., Papadopoulos, P., Parashar, M., Saied, F., Saylor, P.E., Scheel, M.A., Seidel, E., Shapiro, S.L., Shoemaker, D.M., Smarr, L.L., Szilágyi, B., Teukolsky, S.A., van Putten, M.H.P.M., Walker, P., Winicour, J., and York Jr, J.W. (The Binary Black Hole Grand Challenge Alliance), "Gravitational wave extraction and outer boundary conditions by perturbative matching", Phys. Rev. Lett., 80, 1812-1815, (1998). 1, 4.3
4. Abrahams, A.M., Shapiro, S.L., and Teukolsky, S.A., "Calculation of gravitational waveforms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes", Phys. Rev. D, 51(8), 4295-4301, (1995). 1, 4.3
5. Alcubierre, M. et al. (AppleswithApples Alliance), "Toward standard testbeds for numerical relativity", Class. Quantum Grav., 21, 589-613, (2004). 3.5.3, 4
6. Anderson, J.L., "Gravitational radiation damping in systems with compact components", Phys. Rev. D, 36(8), 2301-2313, (1987). 4.3
7. Anderson, J.L., and Hobill, D.W., "Matched analytic-numerical solutions of wave equations", in J.M., Centrella., ed., Dynamical Spacetimes and Numerical Relativity, Proceedings of the Workshop held at Drexel University, October 7-11, 1985, 389-410, (Cambridge University Press, Cambridge, U.K., New York, U.S.A., 1986). 4.3
8. Anderson, J.L., and Hobill, D.W., "Mixed analytic-numerical solutions for a simple radiating system", Gen. Relativ. Gravit., 19(6), 563-580, (1987). 4.3
9. Anderson, J.L., and Hobill, D.W., "A Study of nonlinear radiation damping by matching analytic and numerical solutions", J. Comput. Phys., 75(2), 283-299, (1988). 4.3
10. Anderson, J.L., Kates, R.E., Kegeles, L.S., and Madonna, R.G., "Divergent integrals of post-Newtonian gravity: Nonanalytic terms in the near-zone expansion of a gravitationally radiating system found by matching", Phys. Rev. D, 25(8), 2038-2048, (1982). 4.3
11. Anninos, P., Daues, G., Massó, J., Seidel, E., and Suen, W.-M., "Horizon boundary condition for black hole spacetimes", Phys. Rev. D, 51(10), 5562-5578, (1995). 4.4.3
12. Arnowitt, R., Deser, S., and Misner, C.W., "The dynamics of general relativity", in Witten, L., ed., Gravitation: An Introduction to Current Research, 227-265, (Wiley, New York, U.S.A., 1962). 4
13. Babiuc, M.C., Szilágyi, B., Hawke, I., and Zlochower, Y., "Gravitational wave extraction based on Cauchy-characteristic extraction and characteristic evolution", (2005). URL (cited on 30 July 2005): http://arXiv.org/abs/gr-qc/0501008. 4.3
14. Barreto, W., and Da Silva, A., "Gravitational collapse of a charged and radiating fluid ball in the diffusion limit", Gen. Relativ. Gravit., 28(6), 735-747, (1996). 5.1
15. Barreto, W., and Da Silva, A., "Self-similar and charged spheres in the diffusion approximation", Class. Quantum Grav., 16(6), 1783-1792, (1999). 5.1
16. Barreto, W., Da Silva, A., Gómez, R., Lehner, L., Rosales, L., and Winicour, J., "Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity", Phys. Rev. D, 71(6), 064028-1-12, (2005). 3.9
17. Barreto, W., Gómez, R., Lehner, L., and Winicour, J., "Gravitational Instability of a Kink", Phys. Rev. D, 54(6), 3834-3839, (1996). 3.1
18. Barreto, W., Peralta, C., and Rosales, L., "Equation of state and transport processes in self-similar spheres", Phys. Rev. D, 59, 024008-1-4, (1998). 5.1
19. Bartnik, R., "Einstein equations in the null quasi-spherical gauge", Class. Quantum Grav., 14(8), 2185-2194, (1997). 3.5.1
20. Bartnik, R., "Shear-free null quasi-spherical spacetimes", J. Math. Phys., 38(11), 5774-5791, (1997). 3.5.1
21. Bartnik, R., "Interaction of gravitational waves with a black hole", in De Wit, D., Bracken, A.J., Gould, M.D., and Pearce, P.A., eds., XIIth International Congress of Mathematical Physics (ICMP 1997), Proceedings of the Congress held at the University of Queensland, Brisbane, Australia, July 1997, 3, (International Press, Somerville, U.S.A., 1999). 3.4, 3.5.4, 3.5.6
22. Bartnik, R., "Assessing accuracy in a numerical Einstein solver", in Weinstein, G., and Weikard, R., eds., Differential Equations and Mathematical Physics, Proceedings of an international conference held at the University of Alabama in Birmingham, March 16-20, 1999, vol. 16 of AMS/IP Studies in Advanced Mathematics, 11, (American Mathematical Society; International Press, Providence, U.SA., 2000). 3.5.3
23. Bartnik, R., and Norton, A.H., "Numerical solution of the Einstein equations", in Noye, B.J., Teubner, M.D., and Gill, A.W., eds., Computational Techniques and Applications: CTA C97, 91, (World Scientific, Singapore, 1998). 3.5.3
24. Bartnik, R., and Norton, A.H., "Numerical methods for the Einstein equations in null quasispherical coordinates", SIAM J. Sci. Comput., 22(3), 917-950, (2000). 3.4, 3.4, 3.5.3
25. Bartnik, R., and Norton, A.H., "Numerical Experiments at Null Infinity", Ltd. Notes Phys., 604, 313-326, (2002). 3.5.6
26. Baumgarte, T.W., Shapiro, S.L., and Teukolsky, S.A., "Computing supernova collapse to neutron stars and black holes", Astrophys. J., 443, 717-734, (1995). 5.1
27. Baumgarte, T.W., Shapiro, S.L., and Teukolsky, S.A., "Computing the delayed collapse of hot neutron stars to black holes", Astrophys. J., 458, 680-691, (1996). 5.1
28. Bayliss, A., and Turkel, E., "Radiation boundary conditions for wavelike equations", Commun. Pure Appl. Math., 33, 707-725, (1980). 4.1
29. Berger, B.K., "Numerical Approaches to Spacetime Singularities", Living Rev. Relativity, 5, lrr-2002-1, (2002). URL (cited on July 2005):- http://www.livingreviews.org/lrr-2002-1. 3.1
30. Bičák, J., Reilly, P., and Winicour, J., "Boost-rotation symmetric gravitational null cone data", Gen. Relativ. Gravit., 20(2), 171-181, (1988). 3.5.4, 4.5
31. Bishop, N., Gómez, R., Lehner, L., Maharaj, M., and Winicour, J., "High-Powered Gravitational News", Phys. Rev. D, 56, 6298-6309, (1997). 3.5, 3.5.3, 3.5.4, 4.2, 4.8, 5.3.2
32. Bishop, N.T., "Some aspects of the characteristic initial value problem in numerical relativity", in d'Inverno, R.A., ed., Approaches to Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, Southampton, December 1991, 20-33, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1992). 4.2
33. Bishop, N.T., "Numerical relativity combining the Cauchy and characteristic initial value problem", Class. Quantum Grav., 10(2), 333-341, (1993). 4, 4.2
34. Bishop, N.T., "Linearized solutions of the Einstein equations within a Bondi-Sachs frame-work, and implications for boundary conditions in numerical simulations", Class. Quantum Grav., 22, 2393-2406, (2005). 5.3.2
35. Bishop, N.T., and Deshingkar, S.S., "New approach to calculating the News", Phys. Rev. D, 68(2), 024031-1-6, (2003). 5.3.2
36. Bishop, N.T., Gómez, R., Holvorcem, P.R., Matzner, R.A., Papadopoulos, P., and Winicour, J., "Cauchy-characteristic matching: A new approach to radiation boundary conditions", Phys. Rev. Lett., 76(23), 4303-4306, (1996). 4.2, 4.6
37. Bishop, N.T., Gómez, R., Holvorcem, P.R., Matzner, R.A., Papadopoulos, P., and Winicour, J., "Cauchy-characteristic evolution and waveforms", J. Comput. Phys., 136(1), 140-167, (1997). 4.1, 4.2, 4.6
38. Bishop, N.T., Gömez, R., Husa, S., Lehner, L., and Winicour, J., "Numerical Relativistic Model of a Massive Particle in Orbit near a Schwarzschild Black Hole", Phys. Rev. D, 68(8), 084015-1-12, (2003). 5.3.1, 5.3.2
39. Bishop, N.T., Gómez, R., Isaacson, R.A., Lehner, L., Szilágyi, B., and Winicour, J., "Cauchy-characteristic matching", in Bhawal, B., and Iyer, B.R., eds., Black Holes, Gravitational Radiation and the Universe: Essays in Honour of C. V. Vishveshwara, Fundamental Theories of Physics, 383-408, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1999). 4.2, 4.7
40. Bishop, N.T., Gómez, R., Lehner, L., Maharaj, M., and Winicour, J., "The incorporation of matter into characteristic numerical relativity", Phys. Rev. D, 60(2), 24005-1-11, (1999). 5.3
41. Bishop, N.T., Gómez, R., Lehner, L., Maharaj, M., and Winicour, J., "Characteristic initial data for a star orbiting a black hole", Phys. Rev. D, 72(2), 024002-1-16, (2005). 5.3, 5.3.2
42. Bishop, N.T., Gómez, R., Lehner, L., and Winicour, J., "Cauchy-characteristic extraction in numerical relativity", Phys. Rev. D, 54(10), 6153-6165, (1996). 3.5, 3.5.1, 3.5.3, 3.5.4, 4.2, 4.3
43. Bizoń, P., "Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere", Commun. Math. Phys., 215, 45-56, (2000). 3.1.
44. Blaschak, J., and Kriegsmann, G., "A comparative study of absorbing boundary conditions", J. Comput. Phys., 77, 109-139, (1988). 4.1
45. Bondi, H., "Gravitational waves in general relativity", Nature, 186, 535-535, (1960). 1, 2
46. Bondi, H., van der Burg, M.G.J., and Metzner, A.W.K., "Gravitational waves in general relativity VII. Waves from axi-symmetric isolated systems", Proc. R. Soc. London, Ser. A, 269, 21-52, (1962). 1, 2, 3.3, 3.3, 5.3.2
47. Brady, P.R., Chambers, C.M., and Gonçalves, S.M.C.V., "Phases of Massive Scalar Field Collapse", Phys. Rev. D, 56(10), R6057-R6061, (1997). 3.1
48. Brady, P.R., Chambers, C.M., Krivan, W., and Laguna, P., "Telling tails in the presence of a cosmological constant", Phys. Rev. D, 55(12), 7538-7545, (1997). 3.1
49. Brady, P.R., and Smith, J.D., "Black Hole Singularities: A Numerical Approach", Phys. Rev. Lett., 75(7), 1256-1259, (1995). 3.1
50. Burke, W.L., "Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions", J. Math. Phys., 12(3), 401-418, (1971). 4.3
51. Burko, L.M., "Structure of the Black Hole's Cauchy-Horizon Singularity", Phys. Rev. Lett., 79(25), 4958-4961, (1997). 3.1, 3.1.1
52. Burko, L.M., and Ori, A., "Late-time evolution of nonlinear gravitational collapse", Phys. Rev. D, 56(12), 7820-7832, (1997). 3.1
53. Butler, D.S., "The numerical solution of hyperbolic systems of partial differential equations in three independent variables", Proc. R. Soc. London, Ser. A, 255, 232-252, (1960). 3.2
54. Calabrese, C., Pullin, J., Reula, O.A., Sarbach, O., and Tiglio, M., "Well posed constraint-preserving boundary conditions for the linearized Einstein equations", Commun. Math. Phys., 240(1), 377-395, (2003). 4.1
55. Calabrese, G., Lehner, L., and Tiglio, M., "Constraint-preserving boundary conditions in numerical relativity", Phys. Rev. D, 65(10), 104031-1-13, (2002). 4.1
56. Campanelli, M., Gómez, R., Husa, S., Winicour, J., and Zlochower, Y., "Close limit from a null point of view: the advanced solution", Phys. Rev. D, 63(12), 124013-1-15, (2001). 3.7, 3.7, 3.7.1, 4.3
57. Choptuik, M.W., "'Critical' behavior in massless scalar field collapse", in d'Inverno, R.A., ed., Approaches to Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, Southampton, December 1991, 202, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1992). 3.1.
58. Choptuik, M.W., "Universality and scaling in gravitational collapse of a massless scalar field", Phys. Rev. Lett., 70(1), 9-12, (1993). 3.1, 4.4.2
59. Christodoulou, D., "A mathematical theory of gravitational collapse", Commun. Math. Phys., 109(4), 613-647, (1987). 3.1
60. Christodoulou, D., "The formation of black holes and singularities in spherically symmetric gravitational collapse", Commun. Pure Appl. Math., 44, 339-373, (1991). 3.1
61. Christodoulou, D., "Bounded variation solutions of the spherically symmetric Einstein-scalar field equations", Commun. Pure. Appl. Math., 46, 1131-1220, (1993). 3.1
62. Christodoulou, D., "Examples of naked singularity formation in the gravitational collapse of a scalar field", Ann. Math., 140, 607-653, (1994). 3.1
63. Christodoulou, D., "The instability of naked singularities in the gravitational collapse of a scalar field", Ann. Math. (2), 149, 183-217, (1999). 3.1
64. Christodoulou, D., "On the global initial value problem and the issue of singularities", Class. Quantum Grav., 16, A23-A35, (1999). 3.1
65. Christodoulou, D., and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space, vol. 41 of Princeton Mathematical Series, (Princeton University Press, Princeton, U.S.A., 1993). 3.3
66. Clarke, C.J.S., and d'Inverno, R.A., "Combining Cauchy and characteristic numerical evolutions in curved coordinates", Class. Quantum Grav., 11(6), 1463-1448, (1994). 4.2, 4.4.1.
67. Clarke, C.J.S., d'Inverno, R.A., and Vickers, J.A., "Combining Cauchy and characteristic codes. I. The vacuum cylindrically symmetric problem", Phys. Rev. D, 52(12), 6863-6867, (1995). 3.1, 4.2, 4.4.1
68. Cook, G.B., Huq, M.F., Klasky, S.A., Scheel, M.A., Abrahams, A.M., Anderson, A., Anninos, P., Baumgarte, T.W., Bishop, N.T., Brandt, S.R., Browne, J.C., Camarda, K., Choptuik, M.W., Correll, R.R., Evans, C.R., Finn, L.S., Fox, G.C., Gómez, R., Haupt, T., Kidder, L.E., Laguna, P., Landry, W., Lehner, L., Lenaghan, J., Marsa, R.L., Massó, J., Matzner, R.A., Mitra, S., Papadopoulos, P., Parashar, M., Rezzolla, L., Rupright, M.E., Saied, F., Saylor, P.E., Seidel, E., Shapiro, S.L., Shoemaker, D.M., Smarr, L.L., Suen, W.-M., Szilágyi, B., Teukolsky, S.A., van Putten, M.H.P.M., Walker, P., Winicour, J., and York Jr., J.W. (Binary Black Hole Grand Challenge Alliance), "Boosted Three-Dimensional Black-Hole Evolutions with Singularity Excision", Phys. Rev. Lett., 80, 2512-2516, (1998). 3.3, 4.2
69. Corkill, R.W., and Stewart, J.M., "Numerical relativity II. Numerical methods for the characteristic initial value problem and the evolution of the vacuum field equations for space-times with two Killing vectors", Proc. R. Soc. London, Ser. A, 386, 373-391, (1983). 2, 3.1
70. de Moerloose, J., and de Zutter, D., "Surface integral representation boundary condition for the FDTD method", IEEE Trans. Ant. Prop., 41(7), 890-896, (1993). 4.1
71. Derry, L., Isaacson, R.A., and Winicour, J., "Shear-Free Gravitational Radiation", Phys. Rev., 185(5), 1647-1655, (1969). 3.5.1
72. d'Inverno, R.A., ed., Approaches to Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, Southampton, December 1991, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1992). 2
73. d'Inverno, R.A., Dubal, M.R., and Sarkies, E.A., "Cauchy- characteristic matching for a family of cylindrical vacuum solutions possessing both gravitational degrees of freedom", Class. Quantum Grav., 17(16), 3157-3170, (2000). 4.4.1.
74. d'Inverno, R.A., and Vickers, J.A., "Combining Cauchy and characteristic codes. III. The interface problem in axial symmetry", Phys. Rev. D, 54(8), 4919-4928, (1996). 3.3.3, 4.5
75. d'Inverno, R.A., and Vickers, J.A., "Combining Cauchy and characteristic codes. IV. The characteristic field equations in axial symmetry", Phys. Rev. D, 56(2), 772-784, (1997). 3.3.3, 4.5
76. Dubal, M.R., d'Inverno, R.A., and Clarke, C.J.S., "Combining Cauchy and characteristic codes. II. The interface problem for vacuum cylindrical symmetry", Phys. Rev. D, 52(12), 6868-6881, (1995). 3.1, 4.2, 4.4.1
77. Duff, G.F.D., "Mixed problems for linear systems of first order equations", Can. J. Math., 10, 127, (1958). 4.2
78. Engquist, B., and Majda, A., "Absorbing boundary conditions for the numerical simulation of waves", Math. Comput., 31(139), 629-651, (1977). 4.1
79. Fletcher, S.J., and Lun, A.W.C., "The Kerr spacetime in generalized Bondi-Sachs coordinates", Class. Quantum Grav., 20, 4153-4167, (2003). 3.5.7
80. Font, J.A., "Numerical Hydrodynamics in General Relativity", Living Rev. Relativity, 3, lrr-2000-2, (2000). URL (cited on July 2004): http://www.livingreviews.org/lrr-2003-4. 1, 5.1
81. Frauendiener, J., "Conformal Infinity", Living Rev. Relativity, 7, lrr-2004-1, (2004). URL (cited on October 2005): http://www.livingreviews. org/lrr-2004-1. 2
82. Friedman, J.L., Schleich, K., and Witt, D.M., "Topological Censorship", Phys. Rev. Lett., 71, 1486-1489, (1993). 3.6
83. Friedrich, H., "The asymptotic characteristic initial value problem for Einstein's vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system", Proc. R. Soc. London, Ser. A, 378, 401-421, (1981). 3.3.1, 3.6
84. Friedrich, H., "On the regular and the asymptotic characteristic initial value problem for Einstein's vacuum field equations", Proc. R. Soc. London, Ser. A, 375, 169-184, (1981). 3.6
85. Friedrich, H., "Cauchy problems for the conformal vacuum field equations in general relativity", Commun. Math. Phys., 91(4), 445-472, (1983). 2
86. Friedrich, H., and Nagy, G., "The initial boundary value problem for Einstein's Field equations", Commun. Math. Phys., 201(3), 619-655, (1999). 4.1
87. Friedrich, H., and Stewart, J.M., "Characteristic initial data and wavefront singularities in general relativity", Proc. R. Soc. London, Ser. A, 385, 345-371, (1983). 1, 3.3.1
88. Frittelli, S., and Gómez, R., "Einstein boundary conditions for the 3+1 Einstein equations", Phys. Rev. D, 68(4), 044014-1-6, (2003). 4.1
89. Frittelli, S., and Lehner, L., "Existence and uniqueness of solutions to characteristic evolution in Bondi-Sachs coordinates in general relativity", Phys. Rev. D, 59(8), 084012-1-9, (1999). 3.5.5
90. Garfinkel, D., "Choptuik scaling in null coordinates", Phys. Rev. D, 51(10), 5558-5561, (1995). 3.1, 3.1.1
91. Garfinkel, D., Cutler, C., and Duncan, G.C., "Choptuik scaling in six dimensions", Phys. Rev. D, 60, 104007-1-5, (1999). 3.1
92. Geroch, R., "A Method for Generating Solutions of Einstein's Equations", J. Math. Phys., 12, 918-924, (1971). 3.1
93. Givoli, D., "Non-reflecting boundary conditions", J. Comput. Phys., 94(1), 1-29, (1991). 4.1
94. Gnedin, M.L., and Gnedin, N.Y., "Destruction of the Cauchy Horizon in the Reissner-Nordström Black Hole", Class. Quantum Grav., 10, 1083-1102, (1993). 3.1
95. Goldwirth, D.S., and Piran, T., "Gravitational collapse of massless scalar field and cosmic censorship", Phys. Rev. D, 36(12), 3575-3581, (1987). 3.1, 3.5.2
96. Gómez, R., "Gravitational waveforms with controlled accuracy", Phys. Rev. D, 64(2), 024007-1-8, (2001). 3.5.5
97. Gómez, R., and Frittelli, S., "First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations", Phys. Rev. D, 68(8), 084013-1-6, (2003). 3.5.5
98. Gómez, R., Husa, S., Lehner, L., and Winicour, J., "Gravitational waves from a fissioning white hole", Phys. Rev. D, 66(6), 064019-1-8, (2002). 3.5.5, 3.7.2
99. Gómez, R., Husa, S., and Winicour, J., "Complete null data for a black hole collision", Phys. Rev. D, 64(2), 024010-1-20, (2000). 3.6
100. Gómez, R., Isaacson, R.A., Reilly, P., and Winicour, J., "Post-Newtonian Behavior of the Bondi Mass", Phys. Rev. D, 47(8), 3292-3302, (1993). 3.4
101. Gómez, R., Laguna, P., Papadopoulos, P., and Winicour, J., "Cauchy-characteristic evolution of Einstein-Klein-Gordon Systems", Phys. Rev. D, 54(8), 4719-4727, (1996). 4.4.2
102. Gómez, R., Lehner, L., Marsa, R.L., and Winicour, J., "Moving black holes in 3D", Phys. Rev. D, 57(8), 4778-4788, (1997). 2, 3.5, 3.5.3, 3.5.4, 3.5.7, 4.8
103. Gómez, R., Lehner, L., Marsa, R.L., Winicour, J., Abrahams, A.M., Anderson, A., Anninos, P., Baumgarte, T.W., Bishop, N.T., Brandt, S.R., Browne, J.C., Camarda, K., Choptuik, M.W., Cook, G.B., Correll, R.R., Evans, C.R., Finn, L.S., Fox, G.C., Haupt, T., Huq, M.F., Kidder, L.E., Klasky, S.A., Laguna, P., Landry, W., Lenaghan, J., Massö, J., Matzner, R.A., Mitra, S., Papadopoulos, P., Parashar, M., Rezzolla, L., Rupright, M.E., Saied, F., Saylor, P.E., Scheel, M.A., Seidel, E., Shapiro, S.L., Shoemaker, D., Smarr, L.L., Szilágyi, B., Teukolsky, S.A., van Putten, M.H.P.M., Walker, P., and York Jr, J.W. (The Binary Black Hole Grand Challenge Alliance), "Stable Characteristic Evolution of Generic Three-Dimensional Single-Black-Hole Spacetimes", Phys. Rev. Lett., 80(18), 3915-3918, (1998). 3.5.3
104. Gómez, R., Lehner, L., Papadopoulos, P., and Winicour, J., "The eth formalism in numerical relativity", Class. Quantum Grav., 14(4), 977-990, (1997). 3.5.2
105. Gómez, R., Marsa, R.L., and Winicour, J., "Black hole excision with matching", Phys. Rev. D, 56(10), 6310-6319, (1997). 3.5, 3.5.7, 4.4.3, 4.4.3, 4.8
106. Gómez, R., Papadopoulos, P., and Winicour, J., "Null cone evolution of Axisymmetric Vacuum Spacetimes", J. Math. Phys., 35(8), 4184-4204, (1994). 1, 3.3, 3.5.3, 5.2
107. Gómez, R., Schmidt, B.G., and Winicour, J., "Newman-Penrose Constants and the Tails of Self Gravitating Waves", Phys. Rev. D, 49(6), 2828-2836, (1994). 3.1
108. Gómez, R., and Winicour, J., "Asymptotics of Gravitational Collapse of Scalar Waves", J. Math. Phys., 33(4), 1445-1457, (1992). 3.1, 3.1
109. Gómez, R., and Winicour, J., "Gravitational wave forms at finite distances and at null infinity", Phys. Rev. D, 45(8), 2776-2782, (1992). 4.3
110. Grote, M.J., and Keller, J.B., "Nonreflecting boundary conditions for Maxwell's equations", J. Comput. Phys., 139(2), 327-342, (1998). 4.1
111. Gundlach, C., "Critical Phenomena in Gravitational Collapse", Living Rev. Relativity, 2, lrr-1999-4, (1999). URL (cited on 18 January 2005): http://www.livingreviews.org/lrr-1999-4. 3.1
112. Gundlach, C., and Martín-García, J.M., "Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations", Phys. Rev. D, 70(4), 044032-1-16, (2004). 4.1
113. Gundlach, C., Price, R.H., and Pullin, J., "Late-time behavior of stellar collapse and explosions. I. Linearized perturbations", Phys. Rev. D, 49, 883-889, (1994). 3.1
114. Gundlach, C., Price, R.H., and Pullin, J., "Late-time behavior of stellar collapse and explosions. II. Nonlinear evolution", Phys. Rev. D, 49, 890-899, (1994). 3.1
115. Gustafsson, B., Kreiss, H.-O., and Oliger, J., Time Dependent Problems and Difference Methods, (Wiley, New York, U.S.A., 1995). 4.1
116. Hagstrom, T.M., and Hariharan, S., "Accurate boundary conditions for exterior problems in gas dynamics", Math. Comput., 51(184), 581-597, (1988). 4.1
117. Hamadé, R.S., Horne, J.H., and Stewart, J.M., "Continuous self-similarity and S-duality", Class. Quantum Grav., 13, 2241-2253, (1996). 3.1.
118. Hamadé, R.S., and Stewart, J.M., "The spherically symmetric collapse of a massless scalar field", Class. Quantum Grav., 13, 497-512, (1996). 3.1, 3.1.1.
119. Hayward, S.A., "Dual-null dynamics of the Einstein field", Class. Quantum Grav., 10(4), 779-790, (1993). 3.6
120. Hedstrom, G.W., "Nonreflecting boundary conditions for nonlinear hyperbolic systems", J. Comput. Phys., 30(2), 222-237, (1979). 4.1
121. Higdon, R.L., "Absorbing boundary conditions for difference approximations to the multidimensional wave equation", Math. Comput., 47(176), 437-459, (1986). 4.1
122. Hod, S., "High-order contamination in the tail gravtitational collapse", Phys. Rev. D, 60(10), 104053-1-4, (1999). 3.1.
123. Hod, S., "Wave tails in non-trivial backgrounds", Class. Quantum Grav., 18, 1311-1318, (2001). 3.1
124. Hod, S., "Wave tails in time-dependent backgrounds", Phys. Rev. D, 66 (2), 024001-1-4, (2002). 3.1
125. Hod, S., and Piran, T., "Critical behavior and universality in gravitational collapse of a charged scalar field", Phys. Rev. D, 55(6), 3485-3496, (1997). 3.1
126. Hod, S., and Piran, T., "Late-time evolution of charged gravitational colllapse and decay of charged scalar hair. I", Phys. Rev. D, 58(2), 024017-1-6, (1998). 3.1
127. Hod, S., and Piran, T., "Late-time evolution of charged gravitational colllapse and decay of charged scalar hair. II", Phys. Rev. D, 58(2), 024018-1-6, (1998). 3.1
128. Hod, S., and Piran, T., "Late-time evolution of charged gravitational colllapse and decay of charged scalar hair. III. Nonlinear analysis", Phys. Rev. D, 58(2), 024019-1-6, (1998). 3.1
129. Hod, S., and Piran, T., "Late-time tails in gravitational collapse of a self-interacting (massive) scalar-field and decay of a self-interacting scalar hair", Phys. Rev. D, 58(4), 044018-1-6, (1998). 3.1
130. Hod, S., and Piran, T., "Mass inflation in dynamical gravitational collapse of a charged scalar field", Phys. Rev. Lett., 81(8), 1554-1557, (1998). 3.1
131. Husa, S., "Numerical Relativity with the Conformal Field Equations", in Fernádez-Jambrina, L., and González-Romero, L.M., eds., Current Trends in Relativistic Astrophysics: Theoretical, Numerical, Observational, Proceedings of the 24th Spanish Relativity Meeting on Relativistic Astrophysics, Madrid, 2001, vol. 617 of Lecture Notes in Physics, 159-192, (Springer, Berlin, Germany; New York, U.S.A., 2003). 2
132. Husa, S., Lechner, C., Pürrer, M., Thornburg, J., and Aichelburg, P.C., "Type II critical collapse of a self-gravitating nonlinear σ model", Phys. Rev. D, 62, 104007-1-11, (2000). 3.1
133. Husa, S., and Winicour, J., "Asymmetric merger of black holes", Phys. Rev. D, 60, 084019-1-13, (1999). 2, 3.6, 3.6
134. Husa, S., Zlochower, Y., Gómez, R., and Winicour, J., "Retarded radiation from colliding black holes in the close limit", Phys. Rev. D, 65(8), 084034-1-14, (2002). 3.7, 3.7.1, 4.3
135. Ipser, J.R., and Horwitz, G., "The problem of maximizing functionals in Newtonian stellar dynamics, and its relation to thermodynamic and dynamical stability", Astrophys. J., 232(3), 863-873, (1979). 3.1
136. Isaacson, R.A., Gómez, R., and Winicour, J., "Evolution of Scalar Fields from Characteristic Data", J. Comput. Phys., 98(1), 11-25, (1992). 1
137. Isaacson, R.A., Welling, J.S., and Winicour, J., "Null cone computation of gravitational radiation", J. Math. Phys., 24(7), 1824-1834, (1983). 3.3, 3.3, 3.4, 5
138. Israeli, M., and Orszag, S.A., "Approximation of radiation boundary conditions", J. Comput. Phys., 41(1), 115-135, (1981). 4.1
139. Jiang, H., and Wong, Y.S., "Absorbing boundary conditions for second order hyperbolic equations", J. Comput. Phys., 88(1), 205-231, (1990). 4.1
140. Kates, R.E., and Kegeles, L.S., "Nonanalytic terms in the slow-motion expansion of a radiating scalar field on a Schwarzschild background", Phys. Rev. D, 25(8), 2030-2037, (1982). 4.3
141. Khan, K.A., and Penrose, R., "Scattering of Two Impulsive Gravitational Plane Waves", Nature, 229, 185-186, (1971). 3.1
142. Lehner, L., "A dissipative algorithm for wave-like equations in the characteristic formulation", J. Comput. Phys., 149(1), 59-74, (1999). 3.5.3, 3.5.5
143. Lehner, L., "Matching characteristic codes: exploiting two directions general relativity", Int. J. Mod. Phys. D, 9(4), 459-473, (2000). 3.8, 4.4.3
144. Lehner, L., Bishop, N.T., Gómez, R., Szilágyi, B., and Winicour, J., "Exact solutions for the intrinsic geometry of black hole coalescence", Phys. Rev. D, 60, 044005-1-10, (1999). 2, 3.6, 3.6
145. Lehner, L., Gómez, R., Husa, S., Szilágyi, B., Bishop, N.T., and Winicour, J., "Bagels Form When Black Holes Collide", institutional homepage, Pittsburgh Supercomputing Center. URL (cited on 30 July 2005): http://www.psc.edu/research/graphics/gallery/winicour.html. 1, 3.6
146. Lindman, E.L., "Free-space boundary conditions for the time dependent wave equation", J. Comput. Phys., 18(1), 66-78, (1975). 4.1
147. Linke, F., Font, J.A., Janka, H.-T., Müller, E., and Papadopoulos, P., "Spherical collapse of supermassive stars: Neutrino emission and gamma ray bursts", Astron. Astrophys., 376, 568-579, (2001). 5.1
148. Louisiana State University, "LSU Relativity Group", institutional homepage. URL (cited on 30 July 2005): http://relativity.phys.lsu. edu/. 1, 5.3
149. Lousto, C.O., and Price, R.H., "Understanding initial data for black hole collisions", Phys. Rev. D, 56(10), 6439-6457, (1997). 4.3
150. Marsa, R.L., and Choptuik, M.W., "Black-hole-scalar-field interactions in spherical symmetry", Phys. Rev. D, 54(8), 4929-4943, (1996). 3.1, 4.4.3
151. Matzner, R.A., Seidel, H.E., Shapiro, S.L., Smarr, L.L., Suen, W.-M., Teukolsky, S.A., and Winicour, J., "Geometry of a Black Hole Collision", Science, 270, 941-947, (1995). 2
152. May, M.M., and White, R.H., "Hydrodynamic calculations of general-relativistic collapse", Phys. Rev., 141, 1232-1241, (1966). 5.1
153. Miller, J.C., and Motta, S., "Computations of spherical gravitational collapse using null slicing", Class. Quantum Grav., 6, 185-193, (1989). 5.1
154. Moncrief, V., "Gravitational perturbations of spherically symmetric systems. I The exterior problem", Ann. Phys. (N.Y.), 88, 323-342, (1974). 4.3
155. Müller zum Hagen, H., and Seifert, H.J., "On characteristic initial-value and mixed problems", Gen. Relativ. Gravit., 8(4), 259-301, (1977). 3.6
156. Nagar, A., and Rezzolla, L., "Gauge invariant non-spherical metric perturbations of Schwarzschild spacetime", Class. Quantum Grav., 22(16), R167-R192, (2005). 1, 4.3
157. Nayfeh, A., Perturbation Methods, (Wiley, New York, U.S.A., 1973). 4.3
158. Newman, E.T., and Penrose, R., "An approach to gravitational radiation by a method of spin coefficients", J. Math. Phys., 3(3), 566-578, (1962). 2
159. Newman, E.T., and Penrose, R., "Note on the Bondi-Metzner-Sachs group", J. Math. Phys., 7, 863, (1966). 3.5.2
160. Newman, E.T., and Penrose, R., "New conservation laws for zero rest-mass fields in asymptotically flat space-time", Proc. R. Soc. London, Ser. A, 305, 175-204, (1968). 3.1
161. Oren, Y., and Piran, T., "Collapse of charged scalar fields", Phys. Rev. D, 68(4), 044013-1-12, (2003). 3.1
162. Papadopoulos, P., "Nonlinear harmonic generation in finite amplitude black hole oscillations", Phys. Rev. D, 65(8), 084016-1-11, (2002). 3.3.2, 3.8
163. Papadopoulos, P., and Font, J.A., "Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes", Phys. Rev. D, 61, 024015-1-15, (2000). 5.1
164. Papadopoulos, P., and Font, J.A., "Imprints of accretion on gravitational waves from black holes", Phys. Rev. D, 63(4), 044016-1-5, (2001). 5.1
165. Papadopoulos, P.O., Algorithms for the gravitational characteristic initial value problem, Ph.D. Thesis, (University of Pittsburgh, Pittsburgh, U.S.A., 1994). 3.3, 5.2
166. Penrose, R., "Asymptotic Properties of Fields and Space-Times", Phys. Rev. Lett., 10, 66-68, (1963). 1, 2
167. Penrose, R., "Gravitational collapse: The role of general relativity", Riv. Nuovo Cimento, 1, 252-276, (1969). 3.1
168. Piran, T., "Numerical Codes for Cylindrical General Relativistic Systems", J. Comput. Phys., 35, 254-283, (1980). 4.4.1
169. Piran, T., Safier, P.N., and Katz, J., "Cylindrical gravitational waves with two degrees of freedom: An exact solution", Phys. Rev. D, 34(2), 331-332, (1986). 4.4.1
170. Piran, T., Safier, P.N., and Stark, R.F., "General numerical solution of cylindrical gravitational waves", Phys. Rev. D, 32(12), 3101-3107, (1985). 4.4.1
171. Poisson, E., and Israel, W., "Internal structure of black holes", Phys. Rev. D, 41(6), 1796-1809, (1990). 3.1
172. Pollney, D., Algebraic and numerical techniques in general relativity, Ph.D. Thesis, (University of Southampton, Southampton, U.K., 2000). 3.3.3, 4.5
173. Pretorius, F., and Israel, W., "Quasi-spherical light cones of the Kerr geometry", Class. Quantum Grav., 15, 2289-2301, (1998). 3.5.7
174. Pretorius, F., and Lehner, L., "Adaptive Mesh Refinement for Characteristic Codes", J. Comput. Phys., 198, 10-34, (2004). Related online version (cited on 30 July 2005): http://arXiv.org/abs/gr-qc/0302003. 3.1.1, 3.7, 5.3.1
175. Price, R.H., "Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations", Phys. Rev. D, 5(10), 2419-2438, (1972). 3.1, 3.5.6, 3.7
176. Price, R.H., and Pullin, J., "Colliding black holes: The close limit", Phys. Rev. Lett., 72(21), 3297-3300, (1994). 3.1, 3.6
177. Regge, T., and Wheeler, J.A., "Stability of a Schwarzschild singularity", Phys. Rev., 108(4), 1063-1069, (1957). 4.3
178. Renaut, R.A., "Absorbing boundary conditions, difference operators, and stability", J. Comput. Phys., 102(2), 236-251, (1992). 4.1
179. Rendall, A.D., "Local and Global Existence Theorems for the Einstein Equations", Living Rev. Relativity, 5, lrr-2002-6, (2000). URL (cited on January 2005): http://www.livingreviews.org/lrr-2002-6. 2
180. Rezzolla, L., Abrahams, A.M., Matzner, R.A., Rupright, M.E., and Shapiro, S.L., "Cauchy-perturbative matching and outer boundary conditions: Computational studies", Phys. Rev. D, 59(6), 064001-1-17, (1999). 1, 4.3
181. Rupright, M.E., Abrahams, A.M., and Rezzolla, L., "Cauchy- perturbative matching and outer boundary conditions: Methods and tests", Phys. Rev. D, 58(4), 044005-1-9, (1998). 1, 4.3
182. Ryaben'kii, V., and Tsynkov, S.V., "An Application of the Difference Potentials Method to Solving External Problems in CFD", in Hafez, M., and Oshima, K., eds., Computational Fluid Dynamics Review 1998, vol. 2, (World Scientific, Singapore; River Edge, U.S.A., 1998). 4.1
183. Sachs, R.K., "Asymptotic symmetries in gravitational theory", Phys. Rev., 128, 2851-2864, (1962). 3.4
184. Sachs, R.K., "Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time", Proc. R. Soc. London, Ser. A, 270, 103-126, (1962). 2, 3.3.3
185. Sachs, R.K., "On the characteristic initial value problem in gravitational theory", J. Math. Phys., 3(5), 908-914, (1962). 2, 3.6
186. Scheel, M.A., Shapiro, S.L., and Teukolsky, S.A., "Collapse to black holes in Brans-Dicke theory. I. Horizon boundary conditions for dynamical spacetimes", Phys. Rev. D, 51(8), 4208-4235, (1995). 4.4.3
187. Scheel, M.A., Shapiro, S.L., and Teukolsky, S.A., "Collapse to black holes in Brans-Dicke theory. II. Comparison with general relativity", Phys. Rev. D, 51(8), 4236-4249, (1995). 4.4.3
188. Seidel, E., and Suen, W.-M., "Dynamical evolution of boson stars: Perturbing the ground state", Phys. Rev. D, 42(2), 384-403, (1990). 3.1, 3.9
189. Shapiro, S.L., Teukolsky, S.A., and Winicour, J., "Toroidal Black Holes and Topological Censorship", Phys. Rev. D, 52(11), 6982-6987, (1995). 2
190. Shapiro, S.L., Teukolsky, S.A., and Winicour, J., "Toroidal black holes and topological censorship", Phys. Rev. D, 52(12), 6982-6987, (1995). 3.6
191. Siebel, F., Simulation of axisymmetric flows in the characteristic formulation of general relativity, Ph.D. Thesis, (Technische Universität München, München, Germany, 2002). 5.2
192. Siebel, F., Font, J.A., Müller, E., and Papadopoulos, P., "Simulating the dynamics of relativistic stars via a light-cone approach", Phys. Rev. D, 65(6), 064038-1-15, (2002). 5.2
193. Siebel, F., Font, J.A., Müller, E., and Papadopoulos, P., "Axisymmetric core collapse simulations using characteristic numerical relativity", Phys. Rev. D, 67(12), 124018-1-16, (2003). 5.2, 5.3.2
194. Siebel, F., Font, J.A., and Papadopoulos, P., "Scalar field induced oscillations of relativistic stars and gravitational collapse", Phys. Rev. D, 65(2), 024021-1-10, (2002). 5.1
195. Sod, G.A., Numerical Methods in Fluid Dynamics: Initial and Initial Boundary-Value Problems, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1985). 4.1
196. Sorkin, E., and Piran, T., "Effects of pair creation on charged gravitational collapse", Phys. Rev. D, 63(8), 084006-1-12, (2001). 3.1
197. Sorkin, R.D., "A criterion for the onset of instabilities at a turning point", Astrophys. J., 249(1), 254-257, (1981). 3.1
198. Sperhake, U., Sjödin, K.R.P., and Vickers, J.A., "Dynamic cosmic strings I", Phys. Rev. D, 63, 024011-1-14, (2001). 3.1
199. Sperhake, U., Sjödin, K.R.P., and Vickers, J.A., "Dynamic cosmic strings II: Numerical evolution of excited strings", Phys. Rev. D, 63, 024012-1-15, (2001). 8.1
200. Stark, R.F., and Piran, T., "A General Relativistic Code for Rotating Axisymmetric Configurations and Gravitational Radiation: Numerical Methods and Tests", Comput Phys. Rep., 5, 221-264, (1987). 4.5
201. Stewart, J.M., "Numerical relativity", in Bonnor, W.B., Islam, J.N., and MacCallum, M.A.H., eds., Classical General Relativity, Proceedings of the Conference on Classical (Non-Quantum) General Relativity, City University, London, 21-22 December 1983, 231, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1984). 3.1
202. Stewart, J.M., "The characteristic initial value problem in general relativity", in Winkler, K.H.A., and Norman, M.L., eds., Astrophysical Radiation Hydrodynamics, Proceedings of the NATO Advanced Research Workshop on Astrophysical Radiation Hydrodynamics, Garching, Germany, August 2-13, 1982, vol. 188 of NATO ASI Series. Series C, 531, (Reidel, Dordrecht, Netherlands; Boston, U.S.A., 1986). 2
203. Stewart, J.M., "Numerical relativity III. The Bondi mass revisited", Proc. R. Soc. London, Ser. A, 424, 211-222, (1989). 3.3.1, 3.4
204. Stewart, J.M., "The Cauchy problem and the initial boundary value problem in numerical relativity", Class. Quantum Grav., 15, 2865-2889, (1998). 4.1
205. Stewart, J.M., and Friedrich, H., "Numerical relativity I. The characteristic initial value problem", Proc. R. Soc. London, Ser. A, 384, 427-454, (1982). 1, 3.3.1
206. Szilágyi, B., Cauchy-characteristic matching in general relativity, Ph.D. Thesis, (University of Pittsburgh, Pittsburgh, U.S.A., 2000). 4
207. Szilágyi, B., Gómez, R., Bishop, N.T., and Winicour, J., "Cauchy boundaries in linearized gravitational theory", Phys. Rev. D, 62(10), 104006-1-10, (2000). 4
208. Szilágyi, B., and Winicour, J., "Well-posed initial-boundary evolution in general relativity", Phys. Rev. D, 68(4), 041501-1-5, (2003). 1, 4.1, 4.2, 4.7
209. Tamburino, L.A., and Winicour, J., "Gravitational Fields in Finite and Conformal Bondi Frames", Phys. Rev., 150(4), 1039-1053, (1966). 2, 3.4, 5.1
210. Teukolsky, S.A., "Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations", Astrophys. J., 185, 635-648, (1973). 3.7
211. Teukolsky, S.A., "Linearized quadrupole waves in general relativity and the motion of test particles", Phys. Rev. D, 26(4), 745-750, (1982). 3.3
212. Thompson, K.W., "Time dependent boundary conditions for hyperbolic systems", J. Comput. Phys., 68, 1-24, (1987). 4.1
213. Thornburg, J., "Coordinates and boundary conditions for the general relativistic initial data problem", Class. Quantum Grav., 4(5), 1119-1131, (1987). 4.1
214. Ting, L., and Miksis, M.J., "Exact boundary conditions for scattering problems", J. Acoust. Soc. Am., 80(6), 1825-1827, (1986). 4.1
215. Trefethen, L.N., and Halpern, L., "Well-posedness of one-way wave equations and absorbing boundary conditions", Math. Comput., 47, 421-435, (1986). 4.1
216. Tsynkov, S.V., Artificial Boundary Conditions Based on the Difference Potentials Method, NASA Technical Memorandum, 110265, (NASA Langley Research Center, Hampton, U.S.A., 1996). 4.1
217. University of Canberra, "Canberra Relativity Group", institutional homepage. URL (cited on 30 July 2005): http://relativity.ise. canberra.edu.au/. 1
218. University of Pittsburgh, "Pittsburgh Relativity Group", institutional homepage. URL (cited on 30 July 2005): http://artemis.phyast.pitt. edu/. 1
219. Venter, L.R., and Bishop, N.T., "Numerical validation of the Kerr metric in Bondi-Sachs form", (2005). URL (cited on 30 July 2005): http://arXiv.org/abs/gr-qc/0506077. 3.5.7
220. Wald, R.M., General Relativity, (University of Chicago Press, Chicago, U.S.A., 1984). 4.4.3
221. Weber, J., and Wheeler, J.A., "Reality of the cylindrical gravitational waves of Einstein and Rosen", Proc. R. Soc. London, Ser. A, 29, 509, (1957). 3.1, 4.4.1
222. Winicour, J., "Null infinity from a quasi-Newtonian view", J. Math. Phys., 24(8), 2506-2514, (1983). 1
223. Winicour, J., "The quadrupole radiation formula", Gen. Relativ. Gravit., 19(3), 281-287, (1987). 4.3
224. Winicour, J., "The characteristic treatment of black holes", Prog. Theor. Phys. Suppl., 136, 57-71, (1999). 3.6, 3.6
225. Xanthopoulos, B.C., "Cylindrical waves and cosmic strings of Petrov type D", Phys. Rev. D, 34(12), 3608-3616, (1986). 3.1
226. York Jr, J.W., "Kinematics and Dynamics of General Relativity", in Smarr, L.L., ed., Sources of Gravitational Radiation, Proceedings of the Battelle Seattle Workshop, July 24 - August 4, 1978, 83-126, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1979). 1
227. Zerilli, F.J., "Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics", Phys. Rev. D, 2(10), 2141- 2160, (1970). 4.3
228. Zlochower, Y., Waveforms from colliding black holes, Ph.D. Thesis, (University of Pittsburgh, Pittsburgh, U.S.A., 2002). 1, 3.5.4, 3.7, 3.8, 3.8, 5.3.2
229. Zlochower, Y., Gómez, R., Husa, S., Lehner, L., and Winicour, J., "Mode coupling in the nonlinear response of black holes", Phys. Rev. D, 68(8), 084014-1-16, (2003). 1, 3.3.2, 3.5.4, 3.7, 3.8, 3.8, 5.3.2