A new generalized harmonic evolution system

Classical and Quantum Gravity

Volumn 23, Issue 16, 2006, Pages

  Lindblom, Lee ^a   Scheel, Mark A ^a   Kidder, Lawrence E ^b   Owen, Robert ^a   Rinne, Oliver ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Cornell University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746626494     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/16/S09     Document Type: Article

References (31)

1. Renn J and Sauer T 1998 Heuristics and mathematical representation in Einstein's search for a gravitational field equation History of General Relativity (Einstein Studies vol 7) ed H Goenner, J Renn and J Ritter (Cambridge, MA: Birkhäuser) pp 87-125
2. DeDonder T 1921 La Gravifique Einsteinienne (Paris: Gauthier-Villars)
3. DeDonder T 1927 The Mathematical Theory of Relativity (Cambridge, MA: Massachusetts Institute of Technology)
4. Fock V 1959 The Theory of Space Time and Gravitation (New York: Pergamon)
5. Fourès-Bruhat Y 1952 Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires Acta Math. 88 141-225
6. Bruhat Y 1967 Cauchy problem Gravitation: An Introduction to Current Research ed L Witten (New York: Wiley) pp 130-68
7. Fischer A E and Marsden J E 1972 The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system Commun. Math. Phys. 28 1-38
8. Garfinkle D 2002 Harmonic coordinate method for simulating generic singularities Phys. Rev. D 65 044029
9. Szilgyi B, Schmidt B and Winicour J 2002 Boundary conditions in linearized harmonic gravity Phys. Rev. D 65 064015
10. Szilgyi B and Winicour J 2003 Well-posed initial-boundary evolution in general relativity Phys. Rev. D 68 041501
11. Babiuc M C, Szilgyi B and Winicour J 2006 Testing numerical evolution with the shifted gauge wave Class. Quantum Grav. 23 S321-43 (Preprint gr-qc/0511154)
12. Friedrich H 1985 On the hyperbolicity of Einstein's and other gauge field equations Commun. Math. Phys. 100 525-43
13. Pretorius F 2005 Numerical relativity using a generalized harmonic decomposition Class. Quantum Grav. 22 425-52
14. Pretorius F 2005 Evolution of binary black hole spacetimes Phys. Rev. Lett. 95 121101
15. Gundlach C, Calabrese G, Hinder I and Martin-Garcia J M 2005 Constraint damping in the Z4 formulation and harmonic gauge Class. Quantum Grav. 22 3767-74
16. Bona C, Ledvinka T, Palenzuela C and ek M 2003 General-covariant evolution formalism for numerical relativity Phys. Rev. D 67 104005
17. Friedrich H 2005 On the nonlinearity of the subsidiary systems Class. Quantum Grav. 22 L77
18. Rauch J 1985 Symmetric positive systems with boundary characteristics of constant multiplicity Trans. Am. Math. Soc. 291 167-87
19. Secchi P 1996 The initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity Diff. Integral Eqns 9 671-700
20. Secchi P 1996 Well-posedness of characteristic symmetric hyperbolic systems Arch. Rat. Mech. Anal. 134 155-97
21. Liu T P 1979 Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations J. Diff. Eqns 33 92-111
22. Scheel M A, Erickcek A L, Burko L M, Kidder L E, Pfeiffer H P and Teukolsky S A 2004 3d simulations of linearized scalar fields in Kerr spacetime Phys. Rev. D 69 104006
23. 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
24. Alvi K 2002 First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields Class. Quantum Grav. 19 5153-62
25. Stewart J M 1998 The Cauchy problem and the initial boundary value problem in numerical relativity Class. Quantum Grav. 15 2865-89
26. Calabrese G, Lehner L and Tiglio M 2002 Constraint-preserving boundary conditions in numerical relativity Phys. Rev. D 65 104031
27. Calabrese G, Pullin J, Sarbach O, Tiglio M and Reula O 2003 Well posed constraint-preserving boundary conditions for the linearized Einstein equations Commun. Math. Phys. 240 377-95
28. 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
29. Sarbach O and Tiglio M 2005 Boundary conditions for Einstein's field equations: analytical and numerical analysis J. Hyperbolic Diff. Eqns 2 839-83
30. Gustafsson B, Kreiss H-O and Oliger J 1995 Time Dependent Problems and Difference Methods (Pure and Applied Mathematics) (New York: Wiley)
31. Chandrasekhar S and Detweiler S 1975 The quasi-normal modes of the Schwarzschild black hole Proc. R. Soc. Lond. A 344 441-52