Characteristic evolution and matching

Living Reviews in Relativity

Volumn 4, Issue , 2001, 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: 3242661098     PISSN: 14338351     EISSN: None     Source Type: Journal    
DOI: 10.12942/lrr-2001-3     Document Type: Review

References (158)

1. Abrahams, A. M., and Evans, C. R., "Gauge invariant treatment of gravitational radiation near the source: Analysis and numerical spacetimes", Phys. Rev. D, 42(8), 2585-2594, (1990).
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).
3. Abrahams, A. M., Shapiro, S. L., and Teukolsky, S. A., "Calculation of gravitational waveforms from black hole collisions: Applying perturbation theory to numerical spacetimes", Phys. Rev. D, 51(8), 4295-4301, (1995).
4. Anderson, J. L., "Gravitational radiation damping in systems with compact components", Phys. Rev. D, 36(8), 2301-2313, (1987).
5. Anderson, J. L., and Hobill, D., "Matched analytic-numerical solutions of wave equations", in Centrella, J., ed., Dynamical Spacetimes and Numerical Relativity, 389-410, (Cambridge University Press, Cambridge, 1986).
6. Anderson, J. L., and Hobill, D. W., "Mixed analytic-numerical solutions for a simple radiating system", Gen. Relativ. Gravit., 19(6), 563-580, (1987).
7. 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).
8. Anderson, J. L., Kates, R. E., Kegles, L. S., and Madonna, R., "Divergent integrals of post-Newtonian gravity: Nonanalytic terms in the nearzone expansion of a gravitationally radiating system found by matching", J. Math. Phys., 25(8), 2038-2048, (1982).
9. Anninos, P., Daues, G., Masso, J., Seidel, E., and Suen, W.-M., "Horizon boundary condition for black hole spacetimes", Phys. Rev. D, 51(10), 5562-5578, (1995).
10. Arnowitt, R., Deser, S., and Misner, C. W., "The dynamics of general relativity", in Witten, L., ed., Gravitation - an introduction to current research, 227, (Wiley, New York, 1962).
11. 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).
12. Barreto, W., and Da Silva, A., "Self-similar and charged spheres in the diffusion approximation", Class. Quantum Grav., 16(6), 1783-1792, (1999).
13. Barreto, W., Gómez, R., Lehner, L., and Winicour, J., "Gravitational Instability of a Kink", Phys. Rev. D, 54(6), 3834-3839, (1996).
14. Barreto, W., Peralta, C., and Rosales, R., "Equation of state and transport processes in self-similar spheres", Phys. Rev. D, 59, 024008, (1998).
15. Bartnik, R., "Einstein equations in the null quasi-spherical gauge", Class. Quantum Grav., 14(8), 2185-2194, (1997).
16. Bartnik, R., "Shear-free null quasi-spherical spacetimes", J. Math. Phys., 38(11), 5774-5791, (1997).
17. Bartnik, R., "Interaction of gravitational waves with a black hole", in Bracken, T., and De-Wit, D., eds., XIIth Int'l Congress Math. Phys., 3, (International Press, Hong Kong, 1999).
18. Bartnik, R., "Assessing accuracy in a numerical Einstein solver", in Weinstein, G., and Weikard, R., eds., Differential equations and mathematical physics, 11, (International Press, Cambridge, 2000).
19. 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: CTAC97, 91, (World Scientific, Singapore, 1998).
20. Bartnik, R., and Norton, A. H., "Geometric implementation of spherical harmonics", in Computational Techniques and Applications: CTAC99, J. Austral. Math. Soc., Series B, (2000). To appear.
21. Bartnik, R., and Norton, A. H., "Numerical methods for the Einstein equations in null quasi-spherical coordinates", SIAM J. Sci. Comput., 22(3), 917-950, (2000).
22. Bayliss, A., and Turkel, E., "Radiation boundary conditions for wavelike equations", Commun. Pure Appl. Math., XXXIII, 707-725, (1980).
23. Bicak, J., Reilly, P., and Winicour, J., "Boost-rotation symmetric gravitational null cone data", Gen. Relativ. Gravit., 20(2), 171-181, (1988).
24. Bishop, N. T., "Some aspects of the characteristic initial value problem in numerical relativity", in d'Inverno, R., ed., Approaches to Numerical Relativity, 20-33, (Cambridge University Press, Cambridge,, 1992).
25. Bishop, N. T., "Numerical relativity combining the Cauchy and characteristic initial value problem", Class. Quantum Grav., 10(2), 333-341, (1993).
26. 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).
27. 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).
28. Bishop, N. T., Gómez, R., Isaacson, R. A., Lehner, L., Szilagyi, B., and Winicour, J, "Cauchy Characteristic Matching", in Bhawal, B., and Iyer, B. R., eds., On the Black Hole Trail, chapter 24, 383, (Kluwer, Dordrecht, 1998).
29. 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, (1999).
30. Bishop, N. T., Gómez, R., Lehner, L., Maharaj, M., and Winicour, J., "High-powered Gravitational News", Phys. Rev. D, 56(10), 6298-6309, (1997).
31. Bishop, N. T., Gómez, R., Lehner, L., and Winicour, J., "Cauchycharacteristic extraction in numerical relativity", Phys. Rev. D, 54(10), 6153-6165, (1996).
32. Bizón, P., "Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere", To appear in Commun. Math. Phys.
33. Blaschak, J., and Kriegsmann, G., "A comparative study of absorbing boundary conditions", J. Comput. Phys., 77, 109-139, (1988).
34. Bondi, H., "Gravitational waves in general relativity", Nature, 186, 535- 535, (1960).
35. Bondi, H., van der Burg, M. J. G., 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).
36. Burke, W. L., "Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions", J. Math. Phys., 12(3), 401-418, (1971).
37. 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).
38. Choptuik, M. W., "Critical behavior in massless scalar field collapse", in d'Inverno, R., ed., Approaches to Numerical Relativity, 202, (Cambridge University Press, Cambridge, 1992).
39. Choptuik, M. W., "Universality and scaling in gravitational collapse of a massless scalar field", Phys. Rev. Lett., 70(1), 9-12, (1993).
40. Christodoulou, D., "Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large", Commun. Math. Phys., 106(4), 587-621, (1986).
41. Christodoulou, D., "The problem of a self-gravitating scalar field", Commun. Math. Phys., 105(3), 337-361, (1986).
42. Christodoulou, D., "A mathematical theory of gravitational collapse", Commun. Math. Phys., 109(4), 613-647, (1987).
43. Christodoulou, D., "The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations", Commun. Math. Phys., 109(4), 591-611, (1987).
44. Christodoulou, D., and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space, (Princeton University Press, Princeton, 1993).
45. Clarke, C., and d'Inverno, R., "Combining Cauchy and characteristic numerical evolutions in curved coordinates", Class. Quantum Grav., 11(6), 1463-1448, (1994).
46. Clarke, C., d'Inverno, R., and Vickers, J., "Combining Cauchy and characteristic codes. I. The vacuum cylindrically symmetric problem", Phys. Rev. D, 52(12), 6863-6867, (1995).
47. 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).
48. 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).
49. Derry, L., Isaacson, R., and Winicour, J., "Shear-Free Gravitational Radiation", Phys. Rev., 185(5), 1647-1655, (1969).
50. d'Inverno, R. A., ed., Approaches to Numerical Relativity, (Cambridge University Press, Cambridge, 1992).
51. 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).
52. 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).
53. 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).
54. Dubal, M., d'Inverno, R., and Clarke, C., "Combining Cauchy and characteristic codes. II. The interface problem for vacuum cylindrical symmetry", Phys. Rev. D, 52(12), 6868-6881, (1995).
55. Du , G. F. D., "Mixed problems for linear systems of first order equations", Can. J. Math., 10, 127, (1958).
56. Engquist, B., and Majda, A., "Absorbing boundary conditions for the numerical simulation of waves", Math. Comput., 31(139), 629-651, (1977).
57. Font, J. A., "Numerical hydrodynamics in general relativity", (March, 2000), [Article in Online Journal Living Reviews in Relativity]: cited on 18 January 2001, http://www.livingreviews.org/Articles/Volume3/2000-2font.
58. Friedman, J. L., Schleich, K., and Witt, D. M., "Topological censorship", Phys. Rev. Lett., 71(10), 1486-1489, (1993).
59. Friedrich, H., "The asymptotic characteristic initial value problem for Einstein's vacuum field equations as an initial value problem for a firstorder quasilinear symmetric hyperbolic system", Proc. R. Soc. London, Ser. A, 378, 401-421, (1981).
60. 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).
61. Friedrich, H., and Nagy, G., "The initial boundary value problem for Einstein's Field equations", Commun. Math. Phys., 201(3), 619-655, (1999).
62. 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).
63. Garnkel, D., "Choptuik scaling in null coordinates", Phys. Rev. D, 51(10), 5558-5561, (1995).
64. Garnkel, D., Cutler, C., and Duncan, G. C., "Choptuik scaling in six dimensions", Phys. Rev. D, 580, 104007, (1999).
65. Geroch, R, "A method for generating solutions of Einstein's equations", J. Math. Phys., 12(6), 918-924, (1971).
66. Givoli, D., "Non-reflecting boundary conditions", J. Comput. Phys., 94(1), 1-29, (1991).
67. Goldwirth, D., and Piran, T., "Gravitational collapse of massless scalar field and cosmic censorship", Phys. Rev. D, 36(12), 3575-3581, (1987).
68. Gómez, R., Husa, S., and Winicour, J., "Complete null data for a black hole collision", (September, 2000), [Online Los Alamos Archive Preprint]: cited on 18 January 2001, http://xxx.lanl.gov/abs/gr-qc/0009092.
69. 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).
70. Gómez, R., L., Lehner, Marsa, R., and Winicour, J., "Moving black holes in 3D", Phys. Rev. D, 57(8), 4778-4788, (1997).
71. Gómez, R., Laguna, P., Papadopoulos, P., and Winicour, J., "Cauchycharacteristic evolution of Einstein-Klein-Gordon Systems", Phys. Rev. D, 54(8), 4719-4727, (1996).
72. Gómez, R., Lehner, L., Papadopoulos, P., and Winicour, J., "The eth formalism in numerical relativity", Class. Quantum Grav., 14(4), 977-990, (1997).
73. Gómez, R., Marsa, R., and Winicour, J., "Black hole excision with matching", Phys. Rev. D, 56(10), 6310-6319, (1997).
74. Gómez, R., Papadopoulos, P., and Winicour, J., "Null cone evolution of Axisymmetric Vacuum Spacetimes", J. Math. Phys., 35(8), 4184-4204, (1994).
75. Gómez, R., Schmidt, B., and Winicour, J., "Newman-Penrose Constants and the Tails of Self Gravitating Waves", Phys. Rev. D, 49(6), 2828-2836, (1994).
76. Gómez, R., and Winicour, J., "Asymptotics of Gravitational Collapse of Scalar Waves", J. Math. Phys., 33(4), 1445-1457, (1992).
77. Gómez, R., and Winicour, J., "Gravitational wave forms at finite distances and at null infinity", Phys. Rev. D, 45(8), 2776-2782, (1992).
78. Grote, M. J., and Keller, J. B.., "Nonre ecting boundary conditions for Maxwell's equations", J. Comput. Phys., 139(2), 327-342, (1998).
79. Gundlach, C., "Critical phenomena in gravitational collapse", (December, 1999), [Article in Online Journal Living Reviews in Relativity]: cited on 18 January 2001, http://www.livingreviews.org/Articles/Volume2/1999- 4gundlach.
80. Gundlach, C., Price, R., and Pullin, J., "Late-time behavior of stellar collapse and explosions: I. Linear Perturbations", Phys. Rev. D, 49(2), 883-889, (1994).
81. Gundlach, C., Price, R., and Pullin, J., "Late-time behavior of stellar collapse and explosions: II. Nonlinear Evolution", Phys. Rev. D, 49(2), 890-899, (1994).
82. Hagstrom, T. M., and Hariharan, S., "Accurate boundary conditions for exterior problems in gas dynamics", Math. Comput., 51(184), 581-597, (1988).
83. Hamadé, R., Horne, J. H., and Stewart, J. M., "Continuous Self-similarity and S-duality", Class. Quantum Grav., 13, 2241-2253, (1996).
84. Hamadé, R., and Stewart, J. M., "The spherically symmetric collapse of a massless scalar field", Class. Quantum Grav., 13, 497-512, (1996).
85. Hayward, S. A., "Dual-null dynamics of the Einstein field", Class. Quantum Grav., 10(4), 779-790, (1993).
86. Hedstrom, G. W., "Nonre ecting boundary conditions for nonlinear hyperbolic systems", J. Comput. Phys., 30(2), 222-237, (1979).
87. Higdon, R., "Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation", Math. Comput., 47(176), 437-459, (1986).
88. Husa, S., Lechner, C., Purrer, M., Thornburg, J., and Aichelburg, P. C., "Type II critical collapse of a self-gravitating nonlinear -model", Phys. Rev. D, 62, 104007, (2000).
89. Husa, S., and Winicour, J., "Asymmetric merger of black holes", Phys. Rev. D, 60, 084019, (1999).
90. Ipser, J., 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).
91. Isaacson, R. A., Gómez, R., and Winicour, J., "Evolution of Scalar Fields from Characteristic Data", J. Comput. Phys., 98(1), 11-25, (1992).
92. Isaacson, R. A., Welling, J. S., and Winicour, J., "Null cone computation of gravitational radiation", J. Math. Phys., 24(7), 1824-1834, (1983).
93. Israeli, M., and Orszag, S. A., "Approximation of radiation boundary conditions", J. Comput. Phys., 41(1), 115-135, (1981).
94. Jiang, H., and Wong, Y. S., "Absorbing boundary conditions for second order hyperbolic equations", J. Comput. Phys., 88(1), 205-231, (1990).
95. 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).
96. Khan, K. A., and Penrose, R., "Scattering of two impulsive gravitational plane waves", Nature (London), 229, 185-186, (1971).
97. Lehner, L.., Gravitational radiation from black hole spacetimes, PhD Thesis, (University of Pittsburgh, Pittsburgh, USA, 1998).
98. Lehner, L., "A dissipative algorithm for wave-like equations in the characteristic formulation", J. Comput. Phys., 149(1), 59-74, (1999).
99. Lehner, L., "Matching characteristic codes: exploiting two directions general relativity", Int. J. Mod. Phys. D, 9(4), 459-473, (2000).
100. Lehner, L., Bishop, N. T., Gómez, R., Szilagyi, B., and Winicour, J., "Exact solutions for the intrinsic geometry of black hole coalescence", Phys. Rev. D, 60, 044005, (1999).
101. Lindman, E., "Free-space boundary conditions for the time dependent wave equation", J. Comput. Phys., 18(1), 66-78, (1975).
102. Lousto, C. H., and Price, R. H., "Understanding initial data for black hole collisions", Phys. Rev. D, 56(10), 6439-6457, (1997).
103. Marsa, R. L., and Choptuik, M. W., "Black-hole-scalar-field interactions in spherical symmetry", Phys. Rev. D, 54(8), 4929-4943, (1996).
104. Matzner, R. A., Seidel, H. E., Shapiro, S. L., Smarr, L. L., Suen, W.-M., and Winicour, J., "Geometry of a black hole collision", Science, 270, 941-947, (1995).
105. Nayfeh, A., Perturbation Methods, (Wiley, New York, 1973).
106. 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).
107. Newman, E. T., and Penrose, R., "Note on the Bondi-Metzner-Sachs group", J. Math. Phys., 7, 863, (1966).
108. Newman, E. T., and Penrose, R., "New conservation laws for zero restmass fields in asymptotically at space-time", Proc. R. Soc. London, Ser. A, 305, 175-204, (1968).
109. Papadopoulos, P., and Font, J. A., "Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computation of spherically symmetric spacetimes", Phys. Rev. D, 61, 024015, (2000).
110. Papadopoulos, P., and Font, J. A., "Imprints of accretion on gravitational waves from black holes", Phys. Rev. D, 63, 044016, (2001). For a related online version see: P. Papadopoulos, et al., "Imprints of accretion on gravitational waves from black holes", (September, 2000), [Online Los Alamos Archive Preprint]: cited on 18 January 2001, http://xxx.lanl. gov/abs/gr-qc/0009024.
111. Papadopoulos, P., and Font, J. A., "Imprints of accretion on gravitational waves from black holes", Phys. Rev. D, 63, 044016, (2001). For a related online version see: P. Papadopoulos, et al., "Imprints of accretion on gravitational waves from black holes", (September, 2000), [Online Los Alamos Archive Preprint]: cited on 18 January 2001, http://xxx.lanl.gov/abs/gr-qc/0009024.
112. Penrose, R., "Asymptotic properties of fields and space-times", Phys. Rev. Lett., 10, 21, (1963).
113. Piran, T., "Numerical codes for cylindrical general relativistic systems", J. Comput. Phys., 35(2), 254-283, (1980).
114. 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).
115. Piran, T., Safier, P. N., and Stark, R. N., "General numerical solution of cylindrical gravitational waves", Phys. Rev. D, 32(12), 3101-3107, (1985).
116. Pollney, D., Algebraic and numerical techniques in general relativity, PhD Thesis, (University of Southampton, Southampton, UK, 2000).
117. Price, R. H., "Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations", Phys. Rev. D, 5(10), 2419-2438, (1972).
118. Price, R. H., and Pullin, J., "Colliding black holes: the close limit", Phys. Rev. Lett., 72(21), 3297-3300, (1994).
119. Renaut, R., "Absorbing boundary conditions, difference operators, and stability", J. Comput. Phys., 102(2), 236-251, (1992).
120. Rendall, A., "Local and global existence theorems for the Einstein equations", (January, 2000), [Article in Online Journal Living Reviews in Relativity]: cited on 18 January 2001, http://www.livingreviews.org/ Articles/Volume3/2000-1rendall.
121. 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, volume 2, (World Scientific, Singapore, 1998).
122. Sachs, R. K., "Asymptotic symmetries in gravitational theory", Phys. Rev., 128, 2851-2864, (1962).
123. Sachs, R. K., "Gravitational waves in general relativity VIII. Waves in asymptotically at space-time", Proc. R. Soc. London, Ser. A, 270, 103-126, (1962).
124. Sachs, R. K., "On the characteristic initial value problem in gravitational theory", J. Math. Phys., 3(5), 908-914, (1962).
125. Scheel, M. A., L., Shapiro S., 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).
126. Scheel, M. A., L., Shapiro S., 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).
127. Shapiro, S. L., Teukolsky, S., and Winicour, J., "Toroidal black holes and topological censorship", Phys. Rev. D, 52(12), 6982-6987, (1995).
128. Shapiro, S. L., Teukolsky, S. A., and Winicour, J., "Toroidal Black Holes and Topological Censorship", Phys. Rev. D, 52(11), 6982-6987, (1995).
129. Sod, G. A., Numerical Methods in Fluid Dynamics, (Cambridge University Press, Cambridge, 1985).
130. Sorkin, R., "A criterion for the onset of instability at a turning point", Astrophys. J., 249(1), 254-257, (1981).
131. Sperhake, U., Sj̈odin, K. R. P., and Vickers, J. A., "Dynamic cosmic strings I", Phys. Rev. D, 63, 024011, (2001).
132. Sperhake, U., Sjödin, K. R. P., and Vickers, J. A., "Dynamic cosmic strings II: Numerical evolution of excited strings", Phys. Rev. D, 63, 024012, (2001).
133. 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(5), 221-264, (1987).
134. Stewart, J. M., "Numerical relativity", in Bonnor, W. B., Isham, J. N., and MacCallum, M. A. H., eds., Classical General Relativity, 231, (Cambridge University Press, Cambridge, 1984).
135. Stewart, J. M., "The characteristic initial value problem in general relativity", in Winkler, K.-H. A., and Norman, M. L., eds., Astrophysical Radiation Hydrodynamics, 531, (Reidel, Dordrecht, 1986).
136. Stewart, J. M., "Numerical relativity III. The Bondi mass revisited", Proc. R. Soc. London, Ser. A, 424, 211-222, (1989).
137. Stewart, J. M., and Friedrich, H., "Numerical relativity I. The characteristic initial value problem", Proc. R. Soc. London, Ser. A, 384, 427-454, (1982).
138. Szilágyi, B., Cauchy-characteristic matching in general relativity, PhD Thesis, (University of Pittsburgh, Pittsburgh, USA, 2000).
139. Szilágyi, B., Gómez, R., Bishop, N. T., and Winicour, J., "Cauchy boundaries in linearized gravitational theory", Phys. Rev. D, 62, 104006, (2000).
140. Tamburino, L. A., and Winicour, J., "Gravitational Fields in Finite and Conformal Bondi Frames", Phys. Rev., 150(4), 1039-1053, (1966).
141. Teukolsky, S. A., "Linearized quadrupole waves in general relativity and the motion of test particles", Phys. Rev. D, 26(4), 745-750, (1982).
142. The Binary Black Hole Grand Challenge Alliance, "Boosted threedimensional black hole evolution with singularity excision", Phys. Rev. Lett., 80(12), 2512-2516, (1998).
143. The Binary Black Hole Grand Challenge Alliance, "Gravitational wave extraction and outer boundary conditions by perturbative matching", Phys. Rev. Lett., 80(9), 1812-1815, (1998).
144. The Binary Black Hole Grand Challenge Alliance, "Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes", Phys. Rev. Lett., 80(18), 3915-3918, (1998).
145. Thompson, K. W., "Time=dependent boundary conditions for hyperbolic systems", J. Comput. Phys., 68, 1-24, (1987).
146. Thornburg, J., "Coordinates and boundary conditions for the general relativistic initial data problem", Class. Quantum Grav., 4(5), 1119-1139, (1987).
147. Ting, L., and Miksis, M., "Exact boundary conditions for scattering problems", J. Acoust. Soc. Am., 80(6), 1825-1827, (1986).
148. Trefethen, L., and Halpern, L., "Well-posedness of one-way wave equations and absorbing boundary conditions", Math. Comput., 47, 421-435, (1986).
149. Tsynkov, S. V., Artificial Boundary Conditions Based on the Difference Potentials Method, (NASA, 1996), Report no. 110265. NASA Technical Memorandum.
150. University of Canberra, "Home Page", [Online HTML Document]: cited on 18 January 2001, http://gular.canberra.edu.au/relativity.html.
151. University of Pittsburgh, "Home Page", [Online HTML Document]: cited on 18 January 2001, http://julieta.phyast.pitt.edu/~wwwgr/.
152. Wald, R. M., General Relativity, (University of Chicago Press, Chicago, 1984).
153. 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).
154. Winicour, J., "The Quadrupole Radiation Formula", Gen. Relativ. Gravit., 19(3), 281-287, (1987).
155. Winicour, J., "The Characeristic Traetment of Black Holes", Prog. Theor. Phys. Suppl., 136, 57-71, (1999).
156. Xanthopoulos, B. C., "Cylindrical waves and cosmic strings of Petrov type D", Phys. Rev. D, 34(12), 3608-3616, (1986).
157. York, J., "Kinematics and dynamics of general relativity", in Smarr, L. L., ed., Sources of Gravitational Radiation, 83-126, (Cambridge University Press, Cambridge, 1979).
158. Zum Hagen, M., and Seifert, H., "On characteristic initial value and mixed problems", Gen. Relativ. Gravit., 8(4), 259-301, (1977).