Absorbing boundary conditions for Einstein's field equations

Journal of Physics: Conference Series

Volumn 91, Issue 1, 2007, Pages

  Sarbach, Olivier ^a  

^a UNIVERSIDAD MICHOACANA DE SAN NICOLÁS DE HIDALGO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36749092931     PISSN: 17426588     EISSN: 17426596     Source Type: Conference Proceeding    
DOI: 10.1088/1742-6596/91/1/012005     Document Type: Article

References (71)

1. Givoli D 1991 Non-reflecting boundary conditions J. Comput. Phys. 94 1-29
2. Engquist B and Majda A 1977 Absorbing boundary conditions for the numerical simulation of waves Math. Comput. 31 629-651
3. Bayliss A and Turkel E 1980 Radiation boundary conditions for wave-like equations Comm. Pure Appl. Math. 33 707-725
4. Higdon R L 1986 Absorbing boundary conditions for difference approximations to the multidimensional wave equations Math. Comput. 47 437-459
5. Givoli D 2001 High-order nonreflecting boundary conditions without high-order derivatives J. Comput. Phys. 170 849-870
6. Givoli D and Neta B 2003 High-order non-reflecting boundary scheme for time-dependent waves J. Comput. Phys. 186 24-46
7. Alpert B, Greengard L and Hagstrom T 2000 Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation SIAM J. Numer. Anal. 37 1138-1164
8. Winicour J 2005 Characteristic evolution and matching Living Rev. Relativity, 8, URL (cited on 28 Sep 2006): http://www.livingreviews.org/lrr- 2005-10
9. Choptuik M, Lehner L, Olabarrieta I, Petryk R, Pretorius F and Villegas H 2003 Towards the final fate of an unstable black string Phys. Rev. D 68 044001(1)-044001(11)
10. Pretorius F 2005 Evolution of binary black-hole spacetimes Phys. Rev. Lett. 95 121101(1)-121101(4)
11. Friedrich H 1981 On the regular and asymptotic characteristic initial value problem for Einstein's vacuum field equations Proc. R. Soc. Lond. A 375 169-184
12. Frauendiener J 1998 Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. 2. The evolution equations Phys. Rev. D 58 064003(1)-064003(18)
13. Husa S, Schneemann C, Vogel T and Zenginoglu A 2006 Hyperboloidal data and evolution AIP Conf. Proc. vol 841 p 306-313 28th Spanish Relativity Meeting (ERE05): A Century of Relativity Physics, Oviedo, Asturias, Spain, 6-10 Sep 2005
14. Burke W L 1971 Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions J. Math. Phys. 12 401-418
15. Buchman L T and Sarbach O C A 2006 Towards absorbing outer boundaries in general relativity Class. Quantum Grav. 23 6709-6744
16. Novak J and Bonazzola S 2004 Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates J. Comput. Phys. 197 186-196
17. Bardeen J M and Press W H 1973 Radiation fields in the Schwarzschild background J. Math. Phys. 14 7-19
18. Buchman L T and Sarbach O C A 2007 Improved outer boundary conditions for Einstein's field equations Class. Quantum Grav. 24 S307-S326
19. Lau S R 2004 Rapid evaluation of radiation boundary kernels for time-domain wave propagation on blackholes: theory and numerical methods J. Comput. Phys. 199 376-422
20. Lau S R 2004 Rapid evaluation of radiation boundary kernels for time-domain wave propagation on black holes: implementation and numerical tests Class. Quantum Grav. 21 4147-4192
21. Lau S R 2005 Analytic structure of radiation boundary kernels for blackhole perturbations J. Math. Phys. 46 102503(1)-102503(21)
22. Stewart J M 1998 The Cauchy problem and the initial boundary value problem in numerical relativity Class. Quantum Grav. 15 2865-2889
23. Friedrich H and Nagy G 1999 The initial boundary value problem for Einstein's vacuum field equations Comm. Math. Phys. 201 619-655
24. Szilagyi B, Schmidt B G and Winicour J 2002 Boundary conditions in linearized harmonic gravity Phys. Rev. D 65 064015(1)-064015(15)
25. Szilagyi B and Winicour J 2003 Well-posed initial-boundary evolution in general relativity Phys. Rev. D 68 041501(1)-041501(5)
26. Calabrese G, Pullin J, Reula O, Sarbach O and Tiglio M 2003 Well posed constraint-preserving boundary conditions for the linearized Einstein equations Comm. Math. Phys. 240 377-395
27. Calabrese G and Sarbach O 2003 Detecting ill posed boundary conditions in general relativity J. Math. Phys. 44 3888-3899
28. Calabrese G 2003 Constraint preserving boundary conditions for the linearized Einstein equations PhD Thesis Louisiana State University, http://etd.lsu.edu/docs/available/etd-1105103-100340
29. Frittelli S and Gomez R 2003 Boundary conditions for hyperbolic formulations of the Einstein equations Class. Quantum Grav. 20 2379-2392
30. Frittelli S and Gomez R 2003 Einstein boundary conditions for the 3+1 Einstein equations Phys. Rev. D 68 044014(1)-044014(6)
31. Frittelli S and Gomez R 2004 Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations Phys. Rev. D 69 124020(1)- 124020(10)
32. Frittelli S and Gomez R 2004 Einstein boundary conditions for the Einstein equations in the conformal-traceless decomposition Phys. Rev. D 70 064008(1)-064008(13)
33. Gundlach C and Martín-García J M 2004 Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints Phys. Rev. D 70 044031(1)-044031(14)
34. Gundlach C and Martín-García J M 2004 Symmetric hyperbolic and consistent boundary conditions for second order Einstein equations Phys. Rev. D 70 044032(1)-044032(16)
35. Reula O and Sarbach O 2005 A model problem for the initial-boundary value formulation of Einstein's field equations J. Hyperbolic Differ. Equ. 2 397-435
36. Sarbach O and Tiglio M 2005 Boundary conditions for Einstein's field equations: Mathematical and numerical analysis J. Hyperbolic Differ. Equ. 2 839-883
37. Kidder L E, Lindblom L, Scheel M A, Buchman L T and Pfeiffer H P 2005 Boundary conditions for the Einstein evolution system Phys. Rev. D 71 064020(1)-064020(22)
38. Tarfulea N 2005 Constraint preserving boundary conditions for hyperbolic formulations of Einstein's equations PhD Thesis Minnesota University, gr-qc/0508014
39. Lindblom L, Scheel M A, Kidder L E, Owen R and Rinne O 2006 A new generalized harmonic evolution system Class. Quantum Grav. 23 S447-S462
40. Nagy G and Sarbach O 2006 A minimization problem for the lapse and the initial-boundary value problem for Einstein's field equations Class. Quantum Grav. 23 S477-S504
41. Kreiss H O and Winicour J 2006 Problems which are well-posed in a generalized sense with applications to the Einstein equations Class. Quantum Grav. 23 S405-S420
42. Rinne O 2006 Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations Class. Quantum Grav. 23 6275-6300
43. Arnold D N and Tarfulea N 2006 Boundary conditions for the Einstein-christoffel formulation of Einstein's equations gr-qc/0611010
44. Alekseenko A M 2006 Well-posed initial-boundary value problem for a constrained evolution system and radiation-controlling constraint-preserving boundary conditions gr-qc/0611011
45. Iriondo M S and Reula O A 2002 On free evolution of selfgravitating, spherically symmetric waves Phys. Rev. D 65 044024(1)-044024(11)
46. Calabrese G, Lehner L and Tiglio M 2002 Constraint-preserving boundary conditions in numerical relativity Phys. Rev. D 65 104031(1)-104031(13)
47. Bardeen J M and Buchman L T 2002 Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1d colliding gravitational plane waves Phys. Rev. D 65 064037(1)- 064037(23)
48. Lindblom L, Scheel M A, Pfeiffer H P Kidder L E, Shoemaker D and Teukolsky S A 2004 Controlling the growth of constraints in hyperbolic evolution systems Phys. Rev. D 69 124025(1)-124025(14)
49. Holst M, Lindblom L, Owen R, Pfeiffer H P, Scheel M A and Kidder L E 2004 Optimal constraint projection for hyperbolic evolution systems Phys. Rev. D 70 084017(1)-084017(17)
50. Bona C, Ledvinka T, Palenzuela-Luque C and Zacek M 2005 Constraint-preserving boundary conditions in the Z4 numerical relativity formalism Class. Quantum Grav. 22 2615-2634
51. Rinne O 2005 Axisymmetric numerical relativity PhD Thesis Cambridge University, gr-qc/0601064
52. Babiuc M C, Szilagyi B and Winicour J 2006 Harmonic initial-boundary evolution in general relativity Phys. Rev. D 73 064017(1)-064017(23)
53. Babiuc M C, Kreiss H-O and Winicour J 2007 Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations Phys. Rev. D 75 044002(1)-044002(13)
54. Rinne O, Lindblom L and Scheel M A 2007 Testing outer boundary treatments for the Einstein equations Class. Quantum Grav. 24 4053-4078
55. Scheel M A, Pfeiffer H P, Lindblom L, Kidder L E, Rinne O and Teukolsky S A 2006 Solving Einstein's equations with dual coordinate frames Phys. Rev. D 74 104006(1)-104006(13)
56. Ruiz M, Rinne O and Sarbach O 2007 Outer boundary conditions for Einstein's field equations in harmonic coordinates arXiv:0707.2797 [gr-qc]
57. Regge T and Wheeler J 1957 Stability of a Schwarzschild singularity Phys. Rev. 108 1063-1069
58. Zerilli F 1970 Effective potential for even-parity Regge-Wheeler gravitational perturbation equations Phys. Rev. Lett. 24 737-738
59. Sarbach O and Tiglio M 2001 Gauge invariant perturbations of Schwarzschild black holes in horizon penetrating coordinates Phys. Rev. D 64 084016(1)-084016(15)
60. Bardeen J M 2007 private communication
61. Friedrichs K O 1958 Symmetric positive linear differential equations Commun. Pure Appl. Math. 11 333-418
62. Lax P D and Phillips R S 1960 Local boundary conditions for dissipative symmetric linear differential operators Commun. Pure Appl. Math. 13 427-455
63. Secchi P 1996 Well-posedness of characteristic symmetric hyperbolic systems Arch. Rat. Mech. Anal. 134 155-197
64. Kreiss H O and Lorenz J 1989 Initial-Boundary Value Problems and the Navier-Stokes Equations. Academic Press
65. Kreiss H O 1970 Initial boundary value problems for hyperbolic systems Commun. Pure Appl. Math. 23 277-298
66. Kreiss H O, Reula O, Sarbach O and Winicour J 2007 The Einstein equations, boundaries and integration by parts arXiv:0707.4188 [gr-qc]
67. Sarbach O and Lehner L 2004 No naked singularities in homogeneous, spherically symmetric bubble spacetimes? Phys. Rev. D 69 021901 (1)-021901 (5)
68. Guzmn F S, Lehner L and Sarbach O 2007 Do unbounded bubbles ultimately become fenced inside a black hole? arXiv:0706.3915 [hep-th]
69. Shibata M and Nakamura T 1995 Evolution of three-dimensional gravitational waves: Harmonic slicing case Phys. Rev. D 52 5428-5444
70. Baumgarte T W and Shapiro S L 1999 On the numerical integration of Einstein's field equations Phys. Rev. D 59 024007(1)-024007(7)
71. Beyer H and Sarbach O 2004 On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations Phys. Rev. D 70 104004(1)-104004(11)