Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 62, Issue 12, 2000, Pages 1-15

  Alcubierre, Miguel ^a   Allen, Gabrielle ^a   Brügmann, Bernd ^a   Seidel, Edward ^a,b   Suen, Wai Mo ^c,d  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c WASHINGTON UNIVERSITY   (United States)

^d CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18144365881     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.62.124011     Document Type: Article

References (38)

1. 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.
2. G. Allen, K. Camarda, and E. Seidel, gr-qc/9806036 (1998).
3. P. Anninos, J. Massó, E. Seidel, and W.-M. Suen, Phys. World 9, 43 (1996).
4. B. Brügmann, Int. J. Mod. Phys. D 8, 85 (1999).
5. G. B. Cook et al., Phys. Rev. Lett. 80, 2512 (1998).
6. H. Friedrich, Proc. R. Soc. London A375, 169 (1981).
7. H. Friedrich, Proc. R. Soc. London A378, 401 (1981).
8. Y. Choquet-Bruhat and T. Ruggeri, Commun. Math. Phys. 89, 269 (1983).
9. H. Friedrich, Commun. Math. Phys. 100, 525 (1985).
10. C. Bona and J. Massó, Phys. Rev. Lett. 68, 1097 (1992).
11. C. Bona, J. Massó, E. Seidel, and J. Stela, Phys. Rev. Lett. 75, 600 (1995).
12. Y. Choquet-Bruhat and J. York, C. R. Acad. Sci. Paris 321, 1089 (1995).
13. S. Frittelli and O. Reula, Phys. Rev. Lett. 76, 4667 (1996).
14. A. Abrahams and R. Price, Phys. Rev. D 53, 1972 (1996).
15. H. Friedrich, Class. Quantum Grav. 13, 1451 (1996).
16. M. H. van Putten and D. Eardley, Phys. Rev. D 53, 3056 (1996).
17. A. Abrahams, A. Anderson, Y. Choquet-Bruhat, and J. York, C. R. Acad. Sci. Paris 323, 835 (1996).
18. C. Bona, J. Massó, E. Seidel, and J. Stela, Phys. Rev. D 56, 3405 (1997).
19. A. Abrahams, A. Anderson, Y. Choquet-Bruhat, and J. York, Class. Quantum Grav. 14, A9 (1997).
20. A. Anderson, Y. Choquet-Bruhat, and J. York, Topol. Methods Nonlinear Anal. 10, 353 (1997).
21. C. Bona, J. Massó, E. Seidel, and P. Walker, gr-qc/9804052 (1998).
22. A. Anderson and J. York, Phys. Rev. Lett. 82, 4384 (1999).
23. M. Alcubierre, B. Brügmann, M. Miller, and W.-M. Suen, Phys. Rev. D 60, 064017 (1999).
24. S. Detweiler, Phys. Rev. D 35, 1095 (1987).
25. C. W. Lai et al., report, Physics Department, Chinese University of Hong Kong, 1998.
26. O. Brodbeck, S. Frittelli, P. Hübner, and O. A. Reula, J. Math. Phys. 40, 909 (1999).
27. J. Balakrishna et al., Class. Quantum Grav. 13, L135 (1996).
28. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995).
29. T. W. Baumgarte and S. L. Shapiro, Phys. Rev. D 59, 024007 (1999).
30. A. Arbona, C. Bona, J. Massó, and J. Stela, Phys. Rev. D 60, 104014 (1999).
31. S. Frittelli and O. Reula, J. Math. Phys. 40, 5143 (1999).
32. M. Alcubierre et al., Phys. Rev. D 62, 044034 (2000).
33. M. Alcubierre et al., Phys. Rev. D 61, 041501 (2000).
34. T. W. Baumgarte, S. A. Hughes, and S. L. Shapiro, Phys. Rev. D 60, 087501 (1999).
35. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1962).
36. B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods (Wiley, New York, 1995).
37. P. Anninos et al., Phys. Rev. D 56, 842 (1997).
38. S. Frittelli, Phys. Rev. D 55, 5992 (1997).