Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1D colliding gravitational plane waves

Physical Review D

Volumn 65, Issue 6, 2002, Pages

  Bardeen, J M ^a   Buchman, L T ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; DECOMPOSITION; EVOLUTION; GRAVITATIONAL STRESS; METHODOLOGY; NONLINEAR SYSTEM; WAVEFORM;

EID: 0037087885     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.65.064037     Document Type: Article

References (39)

1. É. É. Flanagan and S. A. Hughes, Phys. Rev. D 57, 4535 (1998).
2. M. W. Choptuik, Phys. Rev. Lett. 70, 9 (1993).
3. H. Friedrich and A. D. Rendall, Lect. Notes Phys. 540, 127 (2000).
4. C. Bona, J. Massó, E. Seidel, and P. Walker, gr-qc/9804052.
5. R. J. LeVeque, Numerical Methods for Conservation Laws (Birkhäuser Verlag, Basel, 1992).
6. O. A. Reula, Living Rev. Relativ. 1998-3 at http:// www.livingreviews. org/
7. R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), pp. 227-265.
8. C. Bona, J. Massó, E. Seidel, and J. Stela, Phys. Rev. D 56, 3405 (1997);
9. Phys. Rev. Lett. 75, 600 (1995);
10. C. Bona and J. Massó, Phys. Rev. Lett., ibid. 68, 1097 (1992).
11. A. Anderson and J. W. York, Jr., Phys. Rev. Lett. 82, 4384 (1999).
12. T. W. Baumgarte and S. L. Shapiro, Phys. Rev. D 59, 024007 (1999).
13. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995).
14. M. Alcubierre et al., Phys. Rev. D 62, 044034 (2000).
15. M. Alcubierre, B. Brügmann, D. Pollney, E. Seidel, and R. Takahashi, Phys. Rev. D 64, 061501 (2001).
16. S. Frittelli and O. A. Reula, Phys. Rev. Lett. 76, 4667 (1996).
17. H. Shinkai and G. Yoneda, gr-qc/0103031.
18. H. Shinkai and G. Yoneda, Class. Quantum Grav. 17, 4799 (2000).
19. G. Yoneda and H. Shinkai, Class. Quantum Grav. 18, 441 (2001).
20. G. Yoneda and H. A. Shinkai, Phys. Rev. D 63, 124019 (2001).
21. L. E. Kidder, M. A. Scheel, and S. A. Teukolsky, Phys. Rev. D 64, 064017 (2001).
22. J. Balakrishna et al., Class. Quantum Grav. 13, L135 (1996).
23. L. Rezzolla, A. M. Abrahams, R. A. Matzner, M. E. Rupright, and S. L. Shapiro, Phys. Rev. D 59, 064001 (1999).
24. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, England, 1986).
25. R. J. LeVeque, J. Comput. Phys. 131, 327 (1997).
26. R. J. LeVeque (private discussion).
27. Y. Choquet-Bruhat and T. Ruggeri, Commun. Math. Phys. 89, 269 (1983).
28. Y. Choquet-Bruhat and J. W. York, C. R. Acad. Sci., Ser. I: Math. 321, 1089 (1995).
29. E. T. Newman and R. Penrose, J. Math. Phys. 3, 566 (1962);
30. E. T. Newman and R. Penrose, J. Math. Phys. 4, 998(E) (1963).
31. R. W. MacCormack, in Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics, edited by M. Holt, Lecture Notes in Physics Vol. 8 (Springer-Verlag, Berlin, 1971).
32. P. Anninos, K. Camarda, J. Massó, E. Seidel, W.-M. Suen, and J. Towns, Phys. Rev. D 52, 2059 (1995).
33. D. S. Bale, R. J. LeVeque, S. Mitran, and J. A. Rossmanith, "A wave propagation method for conservation laws and balance laws with spatially varying flux functions," report (2001).
34. R. J. LeVeque and M. Pelanti, J. Comput. Phys. 172, 572 (2001).
35. R. J. LeVeque, CLAWPACK software. http:// www.amath.washington.edu/ claw
36. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Co., New York, 1973), pp. 943-973.
37. U. Yurtsever, Phys. Rev. D 37, 2790 (1988).
38. U. Yurtsever, Phys. Rev. D 38, 1731 (1988).
39. R. Penrose, Proc. R. Soc. London, Ser. A 284, 159 (1965).