An explicit harmonic code for black-hole evolution using excision

Classical and Quantum Gravity

Volumn 24, Issue 12, 2007, Pages

  Szilágyi, Béla ^a   Pollney, Denis ^a   Rezzolla, Luciano ^a,b   Thornburg, Jonathan ^a   Winicour, Jeffrey ^a,c  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b LOUISIANA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249982087     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/24/12/S18     Document Type: Article

References (54)

1. Detweiler S L 1979 Black holes and gravitational waves: perturbation analysis Sources of Gravitational Radiation ed L Smarr (Cambridge: Cambridge University Press) pp 211-30
2. Hahn S G and Lindquist R W 1964 The two body problem in geometrodynamics Ann. Phys. 29 304-31
3. ade A 1971 Colliding black holes PhD Thesis University of North Carolina at Chapel Hill, Chapel Hill, NC
4. Eppley K R 1975 The numerical evolution of the collision of two black holes PhD Thesis Princeton University, Princeton, NJ
5. Smarr L, ade A, DeWitt B and Eppley K R 1976 Collision of two black holes: theoretical framework Phys. Rev. D 14 2443-52
6. Smarr L 1977 Spacetimes generated by computers: black holes with gravitational radiation Ann. N Y Acad. Sci. 302 569-604
7. Smarr L 1979 Gauge conditions, radiation formulae and the two black hole collision Sources of Gravitational Radiation ed L Smarr (Cambridge: Cambridge University Press) p 245
8. Arnowitt R, Deser S and Misner C W 1962 The dynamics of general relativity Gravitation: An Introduction to Current Research ed L Witten (New York: Wiley) pp 227-65
9. Frittelli S and Gómez R 2000 Ill-posedness in the Einstein equations J. Math. Phys. 41 5535-49
10. Cook G B et al 1998 Boosted three-dimensional black-hole evolutions with singularity excision Phys. Rev. Lett. 80 2512-6
11. Pretorius F 2005 Evolution of binary black hole spacetimes Phys. Rev. Lett. 95 121101
12. Diener P, Herrmann F, Pollney D, Schnetter E, Seidel E, Takahashi R, Thornburg J and Ventrella J 2006 Accurate evolution of orbiting binary black holes Phys. Rev. Lett. 96 121101
13. Campanelli M, Lousto C O, Marronetti P and Zlochower Y 2006 Accurate evolutions of orbiting black-hole binaries without excision Phys. Rev. Lett. 96 111101
14. Baker J G, Centrella J, Choi D-I, Koppitz M and van Meter J 2006 Gravitational wave extraction from an inspiraling configuration of merging black holes Phys. Rev. Lett. 96 111102
15. Gonzles J A, Sperhake U, Brügmann B, Hannam M and Husa S 2007 Total recoil: the maximum kick from nonspinning black-hole binary inspiral Phys. Rev. Lett. 98 091101
16. Herrmann F, Hinder I, Shoemaker D and Laguna P 2007 Unequal mass binary black hole plunges and gravitational recoil Class. Quantum. Grav. 24 533
17. de Donder T 1921 La Gravifique Einsteinienne (Paris: Gauthiers-Villars)
18. Fock V 1959 The Theory of Space, Time, and Gravitation (New York: Pergamon)
19. Choquet-Bruhat Y and Ruggeri T 1983 Hyperbolicity of the 3+1 system of Einstein equations Commun. Math. Phys. 89 269-75
20. Garfinkle D 2002 Harmonic coordinate method for simulating generic singularities Phys. Rev. D 65 044029
21. Szilgyi B, Schmidt B and Winicour J 2002 Boundary conditions in linearized harmonic gravity Phys. Rev. D 65 064015
22. Szilgyi B and Winicour J 2003 Well-posed initial-boundary evolution in general relativity Phys. Rev. D 68 041501
23. Babiuc M C, Szilgyi B and Winicour J 2006 Harmonic initial-boundary evolution in general relativity Phys. Rev. D 73 064017
24. Babiuc M C and Winicour J 2006 Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations Preprint gr-qc/0612051
25. Babiuc M C, Szilgyi B and Winicour J 2006 Testing numerical relativity with the shifted gauge wave Class. Quantum Grav. 23 S319-42
26. Pretorius F 2005 Numerical relativity using a generalized harmonic decomposition Class. Quantum Grav. 22 425-52
27. Pretorius F 2006 Simulation of binary black hole spacetimes with a harmonic evolution scheme Class. Quantum Grav. 23 S529-52
28. Lindblom L, Scheel M A, Kidder L E, Owen R and Rinne O 2006 A new generalized harmonic evolution system Class. Quantum Grav. 23 S447-62
29. Scheel M A, Pfeiffer H P, Lindblom Lee, Kidder L E, Rinne O and Teukolsky S A 2006 Solving Einstein's equations with dual coordinate frames Phys. Rev. D 74 104006
30. Palenzuela C, Olabarrieta I, Lehner L and Liebling S 2006 Head-on collisions of boson stars Preprint gr-qc/0612067
31. Bona C, Ledvinka T and Palenzuela C 2002 A 3+1 covariant suite of numerical relativity evolution systems Phys. Rev. D 66 084013
32. 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 2615-34
33. Thornburg J 1996 Finding apparent horizons in numerical relativity Phys. Rev. D 54 4899-918
34. Thornburg J 2004 A fast apparent-horizon finder for 3-dimensional Cartesian grids in numerical relativity Class. Quantum Grav. 21 743-66
35. Schnetter E, Hawley S H and Hawke I 2004 Evolutions in 3D numerical relativity using fixed mesh refinement Class. Quantum Grav. 21 1465-88
36. Cactus Computational Toolkit. http://www.cactuscode.org
37. Andersson L Private communication
38. Friedrich H 1996 Hyperbolic reductions for Einstein's equations Class. Quantum Grav. 13 1451-69
39. Gundlach C, Martin-Garcia J M, Calabrese G and Hinder I 2005 Constraint damping in the Z4 formulation and harmonic gauge Class. Quantum Grav. 22 3767-74
40. Calabrese G 2005 Finite differencing second order systems describing black hole spacetimes Phys. Rev. D 71 027501
41. Szilgyi B, Kreiss H-O and Winicour J 2005 Modeling the black hole excision problem Phys. Rev. D 71 104035
42. Calabrese G and Gundlach C 2005 Discrete boundary treatment for the shifted wave equation Class. Quantum Grav. 23 S343-68
43. Motamed M, Babiuc M C, Szilgyi B, Kreiss H-O and Winicour J 2006 Finite difference schemes for second order systems describing black holes Phys. Rev. D 73 124008
44. Friedrich H and Nagy G 1999 The initial boundary value problem for Einstein's vacuum field equations Commun. Math. Phys. 201 619-55
45. 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 S405-20
46. Mattsson K and Nordström J 2004 Summation by parts operators for finite difference approximations of second derivatives J. Comput. Phys. 199 503-40
47. Kreiss H-O and Petersson N A 2004 A second order accurate embedded boundary method for the wave equation with Dirichlet data SIAM J. Sci. Comput. 31
48. Baker J, Campanelli M, Lousto C O and Takahashi R 2002 Modeling gravitational radiation from coalescing binary black holes Phys. Rev. D 65 124012
49. Ansorg M 2005 A double-domain spectral method for black hole excision data Phys. Rev. D 72 024018
50. Schnetter E and Krishnan B 2006 Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes Phys. Rev. D 73 021502
51. Ashtekar A and Galloway G 2005 Some uniqueness results for dynamical horizons Adv. Theor. Math. Phys. 9 1-30
52. Andersson L, Mars M and Simon W 2005 Local existence of dynamical and trapping horizons Phys. Rev. Lett. 95 111102
53. Kreiss H O and Lorenz J 1989 Initial-Boundary Value Problems and the Navier-Stokes Equations (New York: Academic)
54. Alcubierre M and Schutz B 1994 Time-symmetric ADI and causal reconnection: stable numerical techniques for hyperbolic systems on moving grids J. Comput. Phys. 112 44