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Slicing conditions for axisymmetric gravitational collapse of Brill waves. (English) Zbl 1431.83007
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C75 Space-time singularities, cosmic censorship, etc.
83C15 Exact solutions to problems in general relativity and gravitational theory
83C35 Gravitational waves
83-08 Computational methods for problems pertaining to relativity and gravitational theory
Full Text: DOI
[1] Eppley, K., Evolution of time-symmetric gravitational waves: initial data and apparent horizons, Phys. Rev. D, 16, 1609-1614, (1977)
[2] Brill, D. R., On the positive definite mass of the bondi-weber-wheeler time-symmetric gravitational waves, Ann. Phys., 7, 466-483, (1959)
[3] Abrahams, A. M.; Evans, C. R., Critical behavior and scaling in vacuum axisymmetric gravitational collapse, Phys. Rev. Lett., 70, 2980-2983, (1993)
[4] Teukolsky, S. A., Linearized quadrupole waves in general relativity and the motion of test particles, Phys. Rev. D, 26, 745-750, (1982)
[5] Choptuik, M. W., Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett., 70, 9-12, (1993)
[6] Gundlach, C.; Martín-García, J. M., Critical phenomena in gravitational collapse, Living Rev. Relativ., 10, 5, (2007) · Zbl 1175.83037
[7] Alcubierre, M.; Allen, G.; Brügmann, B.; Lanfermann, G.; Seidel, E.; Suen, W-M; Tobias, M., Gravitational collapse of gravitational waves in 3d numerical relativity, Phys. Rev. D, 61, (2000)
[8] Garfinkle, D.; Duncan, G. C., Numerical evolution of brill waves, Phys. Rev. D, 63, (2001)
[9] Bona, C.; Massó, J.; Seidel, E.; Stela, J., New formalism for numerical relativity, Phys. Rev. Lett., 75, 600-603, (1995)
[10] Alcubierre, M.; Brügmann, B.; Diener, P.; Koppitz, M.; Pollney, D.; Seidel, E.; Takahashi, R., Gauge conditions for long-term numerical black hole evolutions without excision, Phys. Rev. D, 67, (2003)
[11] Hilditch, D.; Baumgarte, T. W.; Weyhausen, A.; Dietrich, T.; Brügmann, B.; Montero, P. J.; Müller, E., Collapse of nonlinear gravitational waves in moving-puncture coordinates, Phys. Rev. D, 88, (2013)
[12] Hilditch, D.; Weyhausen, A.; Brügmann, B., Pseudospectral method for gravitational wave collapse, Phys. Rev. D, 93, (2016)
[13] Hilditch, D.; Weyhausen, A.; Brügmann, B., Evolutions of centered brill waves with a pseudospectral method, Phys. Rev. D, 96, (2017)
[14] Rinne, O., Constrained evolution in axisymmetry and the gravitational collapse of prolate brill waves, Class. Quantum Grav., 25, (2008) · Zbl 1180.83008
[15] Shibata, M.; Nakamura, T., Evolution of three-dimensional gravitational waves: harmonic slicing case, Phys. Rev. D, 52, 5428-5444, (1995) · Zbl 1250.83027
[16] Baumgarte, T. W.; Shapiro, S. L., On the numerical integration of einstein’s field equations, Phys. Rev. D, 59, (1999) · Zbl 1250.83004
[17] Alcubierre, M., Introduction to 3  +  1 Numerical Relativity, (2008), Oxford: Oxford University Press, Oxford · Zbl 1140.83002
[18] Gundlach, C.; Martín-García, J. M., Well-posedness of formulations of the einstein equations with dynamical lapse and shift conditions, Phys. Rev. D, 74, (2006)
[19] van Meter, J. R.; Baker, J. G.; Koppitz, M.; Choi, D-I, How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture, Phys. Rev. D, 73, (2006)
[20] Boyd, J. P., Spectral methods using rational basis functions on an infinite interval, J. Comput. Phys., 69, 112-142, (1987) · Zbl 0615.65090
[21] Boyd, J. P., Chebyshev and Fourier Spectral Methods, (2001), New York: Dover, New York · Zbl 0994.65128
[22] Anderson, E., LAPACK Users’ Guide, (1999), SIAM: Philadelphia, PA, SIAM · Zbl 0755.65028
[24] Löffler, F., The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics, Class. Quantum Grav., 29, (2012) · Zbl 1247.83003
[26] Goodale, T.; Allen, G.; Lanfermann, G.; Massó, J.; Radke, T.; Seidel, E.; Shalf, J., The Cactus framework and toolkit: design and applications, (2003), Springer: Springer, Berlin · Zbl 1027.65524
[27] Schnetter, E.; Hawley, S. H.; Hawke, I., Evolutions in 3D numerical relativity using fixed mesh refinement, Class. Quantum Grav., 21, 1465-1488, (2004) · Zbl 1047.83002
[28] Berger, M. J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53, 484, (1984) · Zbl 0536.65071
[31] Brown, J. D.; Diener, P.; Sarbach, O.; Schnetter, E.; Tiglio, M., Turduckening black holes: an analytical and computational study, Phys. Rev. D, 79, (2009)
[32] Alcubierre, M.; Brandt, S.; Brügmann, B.; Holz, D.; Seidel, E.; Takahashi, R.; Thornburg, J., Symmetry without symmetry: numerical simulation of axisymmetric systems using Cartesian grids, Int. J. Mod. Phys. D, 10, 273-290, (2001)
[33] van der Vorst, H. A., Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13, 631-644, (1992) · Zbl 0761.65023
[34] Szilágyi, B.; Lindblom, L.; Scheel, M. A., Simulations of binary black hole mergers using spectral methods, Phys. Rev. D, 80, (2009)
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