Dữ Liệu Ban Đầu cho Đối Tượng Tính Toán Tương Đối

Abrahams, A.M., Bernstein, D., Hobill, D., Seidel, E., and Smarr, L., “Numerically generated black-hole spacetimes: Interaction with gravitational waves”, Phys. Rev. D, 45(10), 3544–3558, (May, 1992). 3.2.3 Abrahams, A.M., and Evans, C.R., “Critical Behavior and Scaling in Vacuum Axisymmetric Gravitational Collapse”, Phys. Rev. Lett., 70(20), 2980–2983, (May, 1993). 3 Abrahams, A.M., and Price, R.H., “Black-hole collisions from Brill-Lindquist initial data: Predictions of perturbation theory”, Phys. Rev. D, 53(4), 1972–1976, (February, 1996). For a related online version see: A.M. Abrahams, et al., “Black-hole collisions from Brill-Lindquist initial data: predictions of perturbation theory”, (September, 1995), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9509020. 8 Anderson, A., and York Jr., J.W., “Hamiltonian Time Evolution for General Relativity”, Phys. Rev. Lett., 81(6), 1154–1157, (August, 1998). For a related online version see: A. Anderson, et al., “Hamiltonian Time Evolution for General Relativity”, (July, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9807041. 6 Arbona, A., Bona, C., Carot, J., Mas, L., Massò, J., and Stella, J., “Stuffed black holes”, Phys. Rev. D, 57(4), 2397–2402, (February, 1998). For a related online version see: A. Arbona, et al., “Stuffed Black Holes”, (October, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9710111. 3 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, 1962). 2.1 Asada, H., “Formulation for the internal motion of quasiequilibrium configurations in general relativity”, Phys. Rev. D, 57(12), 7292–7298, (June, 1998). For a related online version see: H. Asada, “Formulation for the internal motion of quasi-equilibrium configurations in general relativity”, (April, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9804003. 15 Bardeen, J.M., “A Variational Principle for Rotating Stars in General Relativity”, Astrophys. J., 162(1), 71–95, (October, 1970). 2.4 Bardeen, J.M., and Wagoner, R.V., “Relativistic Disks. I. Uniform Rotation”, Astrophys. J., 167(3), 359–423, (August, 1971). 2.4 Baumgarte, T.W., “Innermost stable circular orbit of binary black holes”, Phys. Rev. D, 62(2), 024018/1–8, (July, 2000). For a related online version see: T.W. Baumgarte, “The Innermost Stable Circular Orbit of Binary Black Holes”, (April, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0004050. 3.4 Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L., and Teukol-sky, S.A., “Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models”, Phys. Rev. Lett., 79(7), 1182–1185, (August, 1997). For a related online version see: T.W. Baumgarte, et al., “Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models”, (April, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9704024. 13, 15 Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L., and Teukolsky, S.A., “General Relativistic Models of Binary Neutron Stars in Quasiequilibrium”, Phys. Rev. D, 57(12), 7299–7311, (June, 1998). For a related online version see: T.W. Baumgarte, et al., “General Relativis-tic Models of Binary Neutron Stars in Quasiequilibrium”, (September, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9709026. 13, 15 Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L., and Teukolsky, S.A., “The Stability of Relativistic Neutron Stars in Binary Orbit”, Phys. Rev. D, 57(10), 6181–6184, (May, 1998). For a related online version see: T.W. Baumgarte, et al., “The Stability of Relativistic Neutron Stars in Binary Orbit”, (May, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9705023. 15 Bildsen, L., and Cutler, C., “Tidal Interaction of Inspiralling Compact Binaries”, Astrophys. J., 400(1), 175–180, (November, 1992). 15 Bishop, N.T., Isaacson, R., Maharaj, M., and Winicour, J., “Black hole data via a Kerr-Schild approach”, Phys. Rev. D, 57(10), 6113–6118, (May, 1998). For a related online version see: N.T. Bishop, et al., “Black Hole Data via a Kerr-Schild Approach”, (November, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9711076. 3.2.3 Bocquet, M., Bonazzola, S., Gourgoulhon, E., and Novak, J., “Rotating Neutron Star Models With Magnetic Field”, Astron. Astrophys., 301(3), 757–775, (September, 1995). For a related online version see: M. Bocquet, et al., “Rotating Neutron Star Models With Magnetic Field”, (March, 1995), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9503044. 4.2 Bona, C., and Massò, J., “Harmonic synchronizations of spacetime”, Phys. Rev. D, 38(8), 2419–2422, (October, 1988). 3.3.2 Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries”, Phys. Rev. D, 56(12), 7740–7749, (December, 1997). For a related online version see: S. Bonazzola, et al., “A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries”, (October, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9710031. 13, 15 Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “Numerical approach for high precision 3-D relativistic star models”, Phys. Rev. D, 58(10), 104020/1–14, (November, 1998). For a related online version see: S. Bonazzola, et al., “Numerical approach for high precision 3-D relativis-tic star models”, (March, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/astro-ph/9803086. 4.2 Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “Numerical models of irrotational binary neutron stars in general relativity”, Phys. Rev. Lett. , 82(5), 892–895, (February, 1999). For a related online version see: S. Bonazzola, et al., “Numerical models of irrotational binary neutron stars in general relativity”, (October, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9810072. 15 Bonazzola, S., Gourgoulhon, E., Salgado, M., and Marck, J.-A., “Axisym-metric rotating relativistic bodies: a new numerical approach for ‘exact’ solutions”, Astron. Astrophys., 278(2), 421–443, (November, 1993). 2.4, 4.2 Bonazzola, S., and Schneider, J., “An Exact Study of Rigidly and Rapidly Rotating Stars in General Relativity with Application to the Crab Pulsar”, Astrophys. J., 191(1), 273–286, (July, 1974). 2.4, 4.2 Bowen, J.M., “General form for the longitudinal momentum of a spherically symmetric source”, Gen. Relativ. Gravit. , 11(3), 227–231, (October, 1979). 3.2.1, 3.2.1 Bowen, J.M., “General solution for flat-space longitudinal momentum”, Gen. Relativ. Gravit., 14(12), 1183–1191, (December, 1982). 3.2.1, 3.2.1 Bowen, J.M., and York Jr., J.W., “Time-asymmetric initial data for black holes and black-hole collisions”, Phys. Rev. D, 21(8), 2047–2056, (April, 1980). 3.2.1, 3.2.1, 10, 10, 10, 3.2.3 Bowen, J.W., Rauber, J., and York Jr., J.W., “Two black holes with axisymmetric parallel spins: Initial data”, Class. Quantum Grav. , 1(5), 591–610, (September, 1984). 3.2.1 Brandt, S., and Brügmann, B., “A simple construction of initial data for multiple black holes”, Phys. Rev. Lett., 78(19), 3606–3609, (May, 1997). For a related online version see: S. Brandt, et al., “A simple construction of initial data for multiple black holes”, (March, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9703066. 9, 3.2.2, 3.2.2 Brandt, S.R., and Seidel, E., “Evolution of distorted rotating black holes. I: Methods and tests”, Phys. Rev. D, 52(2), 856–869, (July, 1995). For a related online version see: S.R. Brandt, et al., “The Evolution of Distorted Rotating Black Holes I: Methods and Tests”, (December, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9412072. 3.2.3 Brandt, S.R., and Seidel, E., “Evolution of distorted rotating black holes. II: Dynamics and analysis”, Phys. Rev. D, 52(2), 870–886, (July, 1995). For a related online version see: S.R. Brandt, et al., “The Evolution of Distorted Rotating Black Holes II: Dynamics and Analysis”, (December, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9412073. 3.2.3 Brandt, S.R., and Seidel, E., “Evolution of distorted rotating black holes. III: Initial data”, Phys. Rev. D, 54(2), 1403–1416, (July, 1996). For a related online version see: S.R. Brandt, et al., “The Evolution of Distorted Rotating Black Holes III: Initial Data”, (January, 1996), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9601010. 3.2.3 Brill, D.R., and Lindquist, R.W., “Interaction energy in geometrostatics”, Phys. Rev., 131(1), 471–476, (July, 1963). 7, 3.1.2 Butterworth, E.M., “On the Structure and Stability of Rapidly Rotating Fluid Bodies in General Relativity. II. The Structure of Uniformly Rotating Pseudopolytropes”, Astrophys. J., 204(2), 561–572, (March, 1976). 4.2 Butterworth, E.M., “On the Structure and Stability of Rapidly Rotating Fluid Bodies in General Relativity. III. Beyond the Angular Velocity Peak”, Astrophys. J., 231(1), 219–223, (July, 1979). 4.2 Butterworth, E.M., and Ipser, J.R., “Rapidly Rotating Fluid Bodies in General Relativity”, Astrophys. J. Lett., 200(2), L103–L106, (September, 1975). 2.4, 4.2 Butterworth, E.M., and Ipser, J.R., “On the Structure and Stability of Rapidly Rotating Fluid Bodies in General Relativity. I. The Numerical Method for Computing Structure and Its Application to Uniformly Rotating Homogeneous Bodies”, Astrophys. J., 204(1), 200–233, (February, 1976). 4.1, 12, 12, 4.2 Cantor, M., and Kulkarni, A.D., “Physical distinctions between normalized solutions of the two-body problem of general relativity”, Phys. Rev. D, 25(10), 2521–2526, (May, 1982). 8 Choquet-Bruhat, Y., and York Jr., J.W., “The Cauchy problem”, in Held, A., ed., General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, volume 1, 99–172, (Plenum, New York, 1980). 2.1 Cook, G.B., “Initial data for axisymmetric black-hole collisions”, Phys. Rev. D, 44(10), 2983–3000, (November, 1991). 3.1.2, 8, 3.2.1, 10 Cook, G.B., “Three-dimensional initial data for the collision of two black holes II: Quasicircular orbits for equal mass black holes”, Phys. Rev. D, 50(8), 5025–5032, (October, 1994). For a related online version see: G.B. Cook, “Three-dimensional initial data for the collision of two black holes II: Quasicircular orbits for equal mass black holes”, (April, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9404043. 3.4, 11 Cook, G.B., and Abrahams, A.M., “Horizon structure of initial-data sets for axisymmetric two-black-hole collisions”, Phys. Rev. D, 46(2), 702–713, (July, 1992). 3.2.3 Cook, G.B., Choptuik, M.W., Dubal, M.R., Klasky, S., Matzner, R.A., and Oliveira, S.R., “Three-dimensional initial data for the collision of two black holes”, Phys. Rev. D, 47(4), 1471–1490, (February, 1993). 3.2.2 Cook, G.B., and Scheel, M.A., “Well-behaved harmonic time slices of a charged, rotating, boosted black hole”, Phys. Rev. D, 56(8), 4775–4781, (October, 1997). 3.3.1, 3.3.2, 3.3.2 Cook, G.B., Shapiro, S.L., and Teukolsky, S.A., “Spin-up of a rapidly rotating star by angular momentum loss: Effects of general relativity”, Astrophys. J., 398(1), 203–223, (October, 1992). 4.2 Cook, G.B., Shapiro, S.L., and Teukolsky, S.A., “Rapidly rotating neutron stars in general relativity: Realistic equations of state”, Astrophys. J., 424(2), 823–845, (April, 1994). 4.2 Cook, G.B., Shapiro, S.L., and Teukolsky, S.A., “Rapidly rotating polytropes in general relativity”, Astrophys. J., 422(1), 227–242, (February, 1994). 4.2 Cook, G.B., Shapiro, S.L., and Teukolsky, S.A., “Testing a Simplified Version of Einstein’s Equations for Numerical Relativity”, Phys. Rev. D, 53(10), 5533–5540, (May, 1996). For a related online version see: G.B. Cook, et al., “Testing a Simplified Version of Einstein’s Equations for Numerical Relativity”, (December, 1995), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9512009. 2.3, 15 Damour, T., Jaranowski, P., and Schäfer, G., “Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation”, Phys. Rev. D, 62(8), 084011/1–21, (October, 2000). For a related online version see: T. Damour, et al., “On the determination of the last stable orbit for circular general relativis-tic binaries at the third post-Newtonian approximation”, (May, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0005034. 3.4, 11 Doran, C., “A new form of the Kerr solution”, Phys. Rev. D, 61(6), 067503/1–4, (March, 2000). For a related online version see: C. Doran, “A new form of the Kerr solution”, (October, 1999), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9910099. 3.3.3 Flanagan, E.E., “Possible Explanation for Star-Crushing Effect in Binary Neutron Star Simulations”, Phys. Rev. Lett. , 82(7), 1354–1357, (February, 1999). For a related online version see: E.E. Flanagan, “Possible explanation for star-crushing effect in binary neutron star simulations”, (November, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/astro-ph/9811132. 15 Friedman, J.L., and Ipser, J.R., “Errata: “Rapidly rotating relativistic stars””, Philos. Trans. R. Soc. London, Ser. A, 341(1662), 561, (December, 1992). 4.2 Friedman, J.L., and Ipser, J.R., “Rapidly rotating relativistic stars”, Philos. Trans. R. Soc. London, Ser. A, 340(1658), 391–422, (September, 1992). 4.2 Friedman, J.L., Ipser, J.R., and Parker, L., “Rapidly Rotating Neutron Star Models”, Astrophys. J. , 304(1), 115–139, (May, 1986). 4.2 Friedman, J.L., Ipser, J.R., and Sorkin, R.D., “Turning-Point Method for Axisymmetric Stability of Rotating Relativistic Stars”, Astrophys. J., 325(2), 722–274, (February, 1988). 15 Garat, A., and Price, R.H., “Nonexistence of conformally flat slices of the Kerr spacetime”, Phys. Rev. D, 61(12), 124011/1–4, (June, 2000). For a related online version see: A. Garat, et al., “Nonexistence of conformally flat slices of the Kerr spacetime”, (February, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0002013. 3.2.3 Gourgoulhon, E., “Relations between three formalisms for irrotational binary neutron stars in general relativity”, (April, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9804054. 15 Gourgoulhon, E., and Bonazzola, S., “Noncircular axisymmetric stationary spacetimes”, Phys. Rev. D, 48(6), 2635–2652, (September, 1993). 4.2 Gourgoulhon, E., Grandclèment, P., Taniguchi, K., Marck, J.-A., and Bonazzola, S., “Quasiequilibrium sequences of synchronized and irrota-tional binary neutron stars in general relativity. I. Method and tests”, (July, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0007028. Submitted to Phys. Rev. D. 15 Grandclèment, P., Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “A multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources”, (March, 2000), [Online Los Alamos Archive Preprint]: cited on 25 October 2000, http://xxx.lanl.gov/abs/gr-qc/0003072. Submitted to J. Comp. Phys. 15 Gullstrand, A., Arkiv. Mat. Astron. Fys., 16, 1, (1922). 3.3.3 Kley, W., and Schäfer, G., “Relativistic dust disks and the Wilson-Mathews approach”, Phys. Rev. D, 60(2), 027501/1–4, (July, 1999). For a related online version see: W. Kley, et al., “Relativistic dust disks and the Wilson-Mathews approach”, (December, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9812068. 3.2.3 Kochanek, C.S., “Coalescing Binary Neutron Stars”, Astrophys. J., 398(1), 234–247, (October, 1992). 15 Komatsu, H., Eriguchi, Y., and Hachisu, I., “Rapidly rotating general relativistic stars—I. Numerical method and its application to uniformly rotating polytropes”, Mon. Not. R. Astron. Soc., 237(2), 355–379, (March, 1989). 2.4, 4.2 Komatsu, H., Eriguchi, Y., and Hachisu, I., “Rapidly rotating general rela-tivistic stars—II. Differentially rotating polytropes”, Mon. Not. R. Astron. Soc., 239(1), 153–171, (July, 1989). 4.2 Kraus, P., and Wilczek, F., “Some applications of a simple stationary line element for the Schwarzschild geometry”, Mod. Phys. Lett. A, 9(40), 37133719, (December, 1994). For a related online version see: P. Kraus, et al., “A simple stationary line element for the Schwarzschild geometry, and some applications”, (June, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9406042. 3.3.3 Kulkarni, A.D., “Time-asymmetric initial data for the N black hole problem in general relativity”, J. Math. Phys., 25(4), 1028–1034, (April, 1984). 3.2.1, 10 Kulkarni, A.D., Shepley, L.C., and York Jr., J.W., “Initial data for N black holes”, Phys. Lett. A, 96(5), 228–230, (July, 1983). 3.2.1, 10 Lake, K., “A class of quasi-stationary regular line elements for the Schwarzschild geometry”, (July, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9407005. 3.3.3 Lichnerowicz, A., “L’integration des équations de la gravitation relativiste et le problème des n corps”, J. Math. Pures Appl., 23, 37–63, (1944). 2.2 Lindquist, R.W., “Initial-Value Problem on Einstein-Rosen Manifolds”, J. Math. Phys., 4(7), 938–950, (July, 1963). 3.1.2 Lousto, C.O., and Price, R.H., “Improved initial data for black hole collisions”, Phys. Rev. D, 57(2), 1073–1083, (June, 1998). For a related online version see: C.O. Lousto, et al., “Improved initial data for black hole collisions”, (August, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9708022. 3.2.3 Marronetti, P., Mathews, G.J., and Wilson, J.R., “Binary neutron-star systems: From the Newtonian regime to the last stable orbit”, Phys. Rev. D, 58(10), 107503/1–4, (November, 1998). For a related online version see: P. Marronetti, et al., “Binary Neutron-Star Systems: From the Newtonian Regime to the Last Stable Orbit”, (March, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9803093. 15 Marronetti, P., Mathews, G.J., and Wilson, J.R., “Irrotational binary neutron stars in quasiequilibrium”, Phys. Rev. D, 60(8), 087301/1–4, (October, 1999). For a related online version see: P. Marronetti, et al., “Irrotational binary neutron stars in quasiequilibrium”, (June, 1999), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9906088. 15 Marsa, R.L., and Choptuik, M.W., “Black-hole-scalar-field interactions in spherical symmetry”, Phys. Rev. D, 54(8), 4929–4943, (October, 1996). For a related online version see: R.L. Marsa, et al., “Black Hole-Scalar Field Interactions in Spherical Symmetry”, (July, 1996), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9607034. 3.3.1 Martel, K., and Poisson, E., “Regular coordinate systems for Schwarzschild and other spherical spacetimes”, Am. J. Phys., 69(4), 476480, (April, 2001). For a related online version see: K. Martel, et al., “Regular coordinate systems for Schwarzschild and other spherical space-times”, (January, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0001069. 3.3.3 Mathews, G.J., Marronetti, P., and Wilson, J.R., “Relativistic hydrodynamics in close binary systems: Analysis of neutron-star collapse”, Phys. Rev. D, 58(4), 043003/1–13, (August, 1998). For a related online version see: G.J. Mathews, et al., “Relativistic Hydrodynamics in Close Binary Systems: Analysis of Neutron-Star Collapse”, (October, 1997), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9710140. 15 Mathews, G.J., and Wilson, J.R., “Revised relativistic hydrodynamical model for neutron-star binaries”, Phys. Rev. D, 61(12), 127304/14, (June, 2000). For a related online version see: G.J. Mathews, et al., “Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries”, (November, 1999), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9911047. 15 Matzner, R.A., Huq, M.F., and Shoemaker, D., “Initial Data and Coordinates for Multiple Black Hole Systems”, Phys. Rev. D, 59(2), 024015/1–6, (January, 1999). For a related online version see: R.A. Matzner, et al., “Initial Data and Coordinates for Multiple Black Hole Systems”, (May, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9805023. 3.2.3 Misner, C.W., “The Method of Images in Geometrostatics”, Ann. Phys. (N. Y.), 24, 102–117, (October, 1963). 3.1.2, 9, 10 Misner, C.W., Thorne, K.S., and Wheeler, J.A., Gravitation, (W. H. Freeman and Company, New York, New York, 1973). 1.1, 3.3.1 Ó Murchadha, N., and York Jr., J.W., “Existence and uniqueness of solutions of the Hamiltonian constraint of general relativity on compact manifolds”, J. Math. Phys., 14(11), 1551–1557, (November, 1973). 3 Ó Murchadha, N., and York Jr., J.W., “Initial-value problem of general relativity. I. General formulation and physical interpretation”, Phys. Rev. D, 10(2), 428–436, (July, 1974). 2.2.2 Ó Murchadha, N., and York Jr., J.W., “Initial-value problem of general relativity. II. Stability of solution of the initial-value equations”, Phys. Rev. D, 10(2), 437–446, (July, 1974). 3, 2.2.2 Ó Murchadha, N., and York Jr., J.W., “Gravitational Potentials: A Constructive Approach to General Relativity”, Gen. Relativ. Gravit. , 7(3), 257–261, (March, 1976). 2.2.2 Oppenheimer, J.R., and Volkoff, G., “On massive neutron cores”, Phys. Rev., 55(4), 374–381, (February, 1939). 4.2 Painlevé, P., C. R. Acad. Sci., 173, 677, (1921). 3.3.3 Pfeiffer, H.P., Teukolsky, S.A., and Cook, G.B., “Quasi-circular Orbits for Spinning Binary Black Holes”, (June, 2000), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/0006084. 3.2.3, 3.4, 3.4 Rieth, R., “On the validity of Wilson’s approach to general relativity”, in Królak, A., ed., Mathematics of Gravitation. Part II. Gravitational Wave Detection, 71–74, (Polish Academy of Sciences, Institute of Mathematics, Warsaw, 1997). Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation held in Warsaw, February 29–March 30, 1996. 3.2.3, 3.4 Robertson, H.P., and Noonan, T.W., Relativity and Cosmology, (Saunders, London, 1968). 3.3.3 Rowan, S., and Hough, J., “Gravitational Wave Detection by Interfer-ometry (Ground and Space)”, (June, 2000), [Article in Online Journal Living Reviews in Relativity]: cited on 31 October 2000, http://www.livingreviews.org/Articles/Volume3/2000-3hough. 1 Shapiro, S.L., and Teukolsky, S.A., “Gravitational Collapse to Neutron Stars and Black Holes: Computer Generation of Spherical Spacetimes”, Astrophys. J., 235(1), 199–215, (January, 1980). 3 Shapiro, S.L., and Teukolsky, S.A., “Gravitational collapse of rotating spheroids and the formation of naked singularities”, Phys. Rev. D, 45(6), 2006–2012, (March, 1992). 3 Shibata, M., “A relativistic formalism for computation of irrotational binary stars in quasiequilibrium states”, Phys. Rev. D, 58(2), 024012/1–5, (July, 1998). For a related online version see: M. Shibata, “A relativistic formalism for computation of irrotational binary stars in quasi-equilibrium states”, (March, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9803085. 13, 15 Smarr, L., Čadež, A., DeWitt, B., and Eppley, K., “Collision of two black holes: Theoretical framework”, Phys. Rev. D, 14(10), 2443–2452, (November, 1976). 3.1.2 Smarr, L., and York Jr., J.W., “Kinematical conditions in the construction of spacetime”, Phys. Rev. D, 17(10), 2529–2551, (May, 1978). 3.3 Sorkin, R.D., “A Criterion for the Onset of Instabilities at a Turning Point”, Astrophys. J., 249(1), 254–257, (October, 1981). 15 Sorkin, R.D., “A Stability Criterion for Many-Parameter Equilibrium Families”, Astrophys. J., 257(2), 847–854, (June, 1982). 15 Stergioulas, N., “Rotating Stars in Relativity”, (June, 1998), [Article in Online Journal Living Reviews in Relativity]: cited on 18 July 2000, http://www.livingreviews.org/Articles/Volume1/1998-8stergio. 4.2 Stergioulas, N., and Friedman, J.L., “Comparing Models of Rapidly Rotating Relativistic Stars Constructed by Two Numerical Methods”, Astrophys. J., 444(1), 306–311, (May, 1995). For a related online version see: N. Stergioulas, et al., “Comparing Models of Rapidly Rotating Rel-ativistic Stars Constructed by Two Numerical Methods”, (November, 1994), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/astro-ph/9411032. 4.2 Teukolsky, S.A., “Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity”, Astrophys. J., 504(1), 442–449, (September, 1998). For a related online version see: S.A. Teukolsky, “Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity”, (March, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9803082. 13, 14, 15 Thornburg, J., “Coordinate and boundary conditions for the general relativistic initial data problem”, Class. Quantum Grav., 4(5), 1119–1131, (September, 1987). 9 Uryū, K., and Eriguchi, Y., “New numerical method for constructing quasiequilibrium sequences of irrotational binary neutron stars in general relativity”, Phys. Rev. D, 61(12), 124023/1–19, (June, 2000). For a related online version see: K. Uryū, et al., “A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity”, (August, 1999), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9908059. 15 Uryū, K., Shibata, M., and Eriguchi, Y., “Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits: Polytropic equations of state”, Phys. Rev. D, 62(10), 104015/115, (November, 2000). For a related online version see: K. Uryū, et al., “Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits: Polytropic equations of state”, (July, 2000), [Online Los Alamos Archive Preprint]: cited on 25 October 2000, http://xxx.lanl.gov/abs/gr-qc/0007042. 15 Wilson, J.R., “Models of Differentially Rotating Stars”, Astrophys. J., 176(1), 273–286, (August, 1972). 4.2 Wilson, J.R., and Mathews, G.J., “Relativistic Hydrodynamics”, in Evans, C.R., Finn, L.S., and Hobill, D.W., eds., Frontiers in Numerical Relativity, 306–314, (Cambridge University Press, Cambridge, England, 1989). 2.3, 13, 15 Wilson, J.R., and Mathews, G.J., “Instabilities in close neutron star binaries”, Phys. Rev. Lett., 75(23), 4161–4164, (December, 1995). 13, 15 Wilson, J.R., Mathews, G.J., and Marronetti, P., “Relativistic Numerical Method for Close Neutron Star Binaries”, Phys. Rev. D, 54(2), 13171331, (July, 1996). For a related online version see: J.R. Wilson, et al., “Relativistic Numerical Method for Close Neutron Star Binaries”, (January, 1996), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9601017. 13, 15 York Jr., J.W., “Gravitational degrees of freedom and the initial-value problem”, Phys. Rev. Lett., 26(26), 1656–1658, (June, 1971). 3, 2.2 York Jr., J.W., “Role of conformal three-geometry in the dynamics of gravitation”, Phys. Rev. Lett., 28(16), 1082–1085, (April, 1972). 3, 2.2 York Jr., J.W., “Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativity”, J. Math. Phys., 14(4), 456–464, (April, 1973). 2.2 York Jr., J.W., “Covariant decompositions of symmetric tensors in the theory of gravitation”, Ann. Inst. Henri Poincare, A, 21(4), 319–332, (1974). 2.2 York Jr., J.W., “Kinematics and Dynamics of General Relativity”, in Smarr, L.L., ed., Sources of Gravitational Radiation, 83–126, (Cambridge University Press, Cambridge, England, 1979). 2.1, 3, 2.2.1 York Jr., J.W., “Energy and Momentum of the Gravitational Field”, in Tipler, F.J., ed., Essays in General Relativity, 39–58, (Academic, New York, 1980). 3.2.1, 3.2.3 York Jr., J.W., “Initial data for N black holes”, Physica (Utrecht), 124A(1-3), 629–637, (March, 1984). 3.2.1, 10 York Jr., J.W., “Initial Data for Collisions of Black Holes and Other Gravitational Miscellany”, in Evans, C.R., Finn, L.S., and Hobill, D.W., eds., Frontiers in Numerical Relativity, 89–109, (Cambridge University Press, Cambridge, England, 1989). 10 York Jr., J.W., “Conformal ‘thin-sandwich’ data for the initial-value problem of general relativity”, Phys. Rev. Lett., 82(7), 1350–1353, (February, 1999). For a related online version see: J.W. York Jr., “Conformal ‘thin-sandwich’ data for the initial-value problem of general relativity”, (October, 1998), [Online Los Alamos Archive Preprint]: cited on 18 July 2000, http://xxx.lanl.gov/abs/gr-qc/9810051. 2.3 York Jr., J.W., and Piran, T., “The Initial Value Problem and Beyond”, in Matzner, R.A., and Shepley, L.C., eds., Spacetime and Geometry, 147–176, (University of Texas, Austin, 1982). 2.2.1, 10