Causal differencing in ADM and conformal ADM formulations: A comparison in spherical symmetry

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 62, Issue 8, 2000, Pages 1-10

  Lehner, Luis ^a   Huq, Mijan ^b   Garrison, David ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750813916     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.62.084016     Document Type: Article

References (38)

1. M. Huq, in Proceedings of the BBH Grand Challenge Meeting, Pittsburgh, Pennsylvania, 1997 (unpublished).
2. G. Gook and M. Scheel, in Proceedings of the BBH Grand Challenge Meeting, Austin, Texas, 1998 (unpublished).
3. J. Thornburg, Class. Quantum Grav. 14, 1119 (1987).
4. For instance, H. Friedrich, Proc. R. Soc. London A375, 169 (1981); S. Frittelli and O. Reula, Phys. Rev. Lett. 76, 4667 (1996); A. Anderson and J. York, ibid. 82, 4384 (1999). [For a detailed list of hyperbolic formulations see O. Reula, "Hyperbolic Methods for Einstein's equations," Living Reviews (1998).]
5. For instance, H. Friedrich, Proc. R. Soc. London A375, 169 (1981); S. Frittelli and O. Reula, Phys. Rev. Lett. 76, 4667 (1996); A. Anderson and J. York, ibid. 82, 4384 (1999). [For a detailed list of hyperbolic formulations see O. Reula, "Hyperbolic Methods for Einstein's equations," Living Reviews (1998).]
6. For instance, H. Friedrich, Proc. R. Soc. London A375, 169 (1981); S. Frittelli and O. Reula, Phys. Rev. Lett. 76, 4667 (1996); A. Anderson and J. York, ibid. 82, 4384 (1999). [For a detailed list of hyperbolic formulations see O. Reula, "Hyperbolic Methods for Einstein's equations," Living Reviews (1998).]
7. For instance, H. Friedrich, Proc. R. Soc. London A375, 169 (1981); S. Frittelli and O. Reula, Phys. Rev. Lett. 76, 4667 (1996); A. Anderson and J. York, ibid. 82, 4384 (1999). [For a detailed list of hyperbolic formulations see O. Reula, "Hyperbolic Methods for Einstein's equations," Living Reviews (1998).]
8. C. Bona, J. Masso, E. Seidel, and J. Stela, Phys. Rev. D 56, 3405 (1997).
9. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995).
10. T. Baumgarte and S. Shapiro, Phys. Rev. D 59, 024007 (1999).
11. S. Frittelli and O. Reula, J. Math. Phys. 40, 5143 (1999).
12. L. L. Smarr and J. W. York, Phys. Rev. D 17, 2529 (1978); P. R. Brady, J. D. Creighton, and K. S. Thorne, ibid. 58, 061501 (1998); C. Gundlach and D. Garfinkle, Class. Quantum Grav. 16, 4111 (1999).
13. L. L. Smarr and J. W. York, Phys. Rev. D 17, 2529 (1978); P. R. Brady, J. D. Creighton, and K. S. Thorne, ibid. 58, 061501 (1998); C. Gundlach and D. Garfinkle, Class. Quantum Grav. 16, 4111 (1999).
14. L. L. Smarr and J. W. York, Phys. Rev. D 17, 2529 (1978); P. R. Brady, J. D. Creighton, and K. S. Thorne, ibid. 58, 061501 (1998); C. Gundlach and D. Garfinkle, Class. Quantum Grav. 16, 4111 (1999).
15. For a recent review see J. Font, "Numerical Hydrodynamics in General Relativity," Living Reviews (2000).
16. K. Oohara and T. Nakamura, Prog. Theor. Phys. Suppl. 136, 270 (1999).
17. M. Alcubierre, G. Allen, B. Brügmann, T. Dramlitsch, J. Font, P. Papadopoulos, E. Seidel, N. Stergioulas, W. M. Suen, and R. Takahashi, Phys. Rev. D 62, 044034 (2000).
18. B. Brügmann, Int. J. Mod. Phys. D 8, 85 (1999).
19. The Binary Black Hole Grand Challenge Alliance, Phys. Rev. Lett. 80, 2512 (1998).
20. R. Marsa and M. Choptuik, Phys. Rev. D 54, 4929 (1996).
21. C. Misner, K. S. Thorne, and J. Wheeler, Gravitation (Freeman, San Francisco, 1973).
22. M. Alcubierre, G. Allen, B. Buegman, E. Seidel, and W. M. Suen, "Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity," gr-qc/9908079, 1999.
23. E. Seidel and W. M. Suen, Phys. Rev. Lett. 69, 1845 (1992).
24. M. Alcubierre and B. Schutz, J. Comput. Phys. 112, 44 (1994).
25. C. Gundlach and P. Walker, Class. Quantum Grav. 16, 991 (1999).
26. M. Scheel, T. Baumgarte, G. Cook, S. Shapiro, and S. Teukolsky, Phys. Rev. D 56, 6320 (1997).
27. M. Huq and R. Matzner (unpublished).
28. URL http://www.astro.psu.edu/users/nr/Agave/
29. S. Teukolsky, Phys. Rev. D 61, 087501 (2000).
30. A. E. Eddington, Nature (London) 113, 192 (1924); D. Finkelstein, Phys. Rev. 110, 965 (1958).
31. A. E. Eddington, Nature (London) 113, 192 (1924); D. Finkelstein, Phys. Rev. 110, 965 (1958).
32. L. Lehner, M. Huq, M. Anderson, E. Bonning, D. Schaefer, and R. Matzner, Phys. Rev. D 62, 044037 (2000).
33. R. Gomez, in Proceedings of the BBH Grand Challenge Meeting, Los Alamos, New Mexico, 1997.
34. B. Gustaffson, H. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods (Wiley, New York, 1995).
35. A. Lichnerowicz, J. Math. Pures Appl. 23, 37 (1944).
36. J. W. York, in Sources of Gravitational Radiation, edited by L. Smarr (Cambridge University Press, Cambridge, England, 1979).
37. R. Gomez, L. Lehner, R. Marsa, and J. Winicour, Phys. Rev. D 57, 4778 (1998).
38. J. Thornburg, "A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes II: Time Evolution," gr-qc/9906022, 1999.