Physics and initial data for multiple black hole spacetimes

Physical Review D

Volumn 68, Issue 4, 2003, Pages

  Bonning, Erin ^a   Marronetti, Pedro ^a,b   Neilsen, David ^a,c   Matzner, Richard ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ARTICLE; ASTRONOMY; GRAVITY; MATHEMATICAL ANALYSIS; PARAMETER; PHYSICAL CHEMISTRY; PHYSICS; RADIATION; WAVEFORM;

EID: 0141656330     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.044019     Document Type: Article

References (53)

1. G.B. Cook, Phys. Rev. D 50, 5025 (1994).
2. H.P. Pfeiffer, S.A. Teukolsky, and G.B. Cook, Phys. Rev. D 62, 104018 (2000).
3. T.W. Baumgarte, Phys. Rev. D 62, 024018 (2000).
4. E. Gourgoulhon, P. Grandclement, and S. Bonazzola, Phys. Rev. D 65, 044020 (2002).
5. P. Grandclement, E. Gourgoulhon, and S. Bonazzola, Phys. Rev. D 65, 044021 (2002), and references therein.
6. E. Gourgoulhon, P. Grandclement, and S. Bonazzola, Int. J. Mod. Phys. A 17, 2689 (2002).
7. G.B. Cook, Phys. Rev. D 65, 084003 (2002).
8. H.P. Pfeiffer, G.B. Cook, and S.A. Teukolsky, Phys. Rev. D 66, 024047 (2002).
9. G.B. Cook, Living Rev. Relativ. 3, 5 (2000).
10. P. Peters and J. Matthews, Phys. Rev. 131, 435 (1963).
11. T. Mora and C.M. Will, Phys. Rev. D 66, 101501(R) (2002).
12. D.M. Shoemaker, M.F. Huq, and R.A. Matzner, Phys. Rev. D 62, 124005 (2000).
13. M.F. Huq, M.W. Choptuik, and R.A. Matzner, Phys. Rev. D 66, 084024 (2002).
14. O. Dreyer, B. Krishnan, D. Shoemaker, and E. Schnetter, Phys. Rev. D 67, 024018 (2003), and references therein.
15. S.A. Caveny, Ph.D. dissertation, University of Texas at Austin, 2002.
16. S.A. Caveny, M. Anderson, and R.A. Matzner, Phys. Rev. D (to be published), gr-qc/0303099.
17. R. Arnowitt, S. Deser, and C. Misner, in Gravitation, an Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
18. J. York and T. Piran, Spacetime and Geometry: The Alfred Schild Lectures, edited by R. Matzner and L. Shepley (University of Texas Press, Austin, TX, 1982);
19. G. Cook, Ph.D. dissertation, The University of North Carolina at Chapel Hill, 1990.
20. N.Ó. Murchadha and J.W. York, Jr., Phys. Rev. D 10, 428 (1974);
21. N.Ó. Murchadha and J.W. York, Jr., Phys. Rev. D 10, 437 (1974);
22. Gen. Relativ. Gravit. 7, 257 (1976).
23. J.W. York, Jr., Phys. Rev. Lett. 82, 1350 (1999).
24. J.R. Wilson and G.J. Mathews, Phys. Rev. Lett. 75, 4161 (1995);
25. J.R. Wilson, G.J. Mathews, and P. Marronetti, Phys. Rev. D 54, 1317 (1996).
26. J.M. Bowen and J.W. York, Phys. Rev. D 21, 2047 (1980).
27. A. Garat and R.H. Price, Phys. Rev. D 61, 124011 (2000).
28. N. Jansen, P. Diener, A. Khokhlov, and I. Novikov, Class. Quantum Grav. 20, 51 (2003).
29. R. Matzner, M.F. Huq, and D. Shoemaker, Phys. Rev. D 59, 024015 1999).
30. R. Kerr and A. Schild, in Applications of Nonlinear Partial Differential Equations in Mathematical Physics, Proceedings of Symposia B Applied Math., Vol XVII American Mathematical Society, Providence, RI, (1965);
31. Atti del Congressa-Sulla Relitivita Generale: Problemi Dell'Energia E Onde Gravitazionala, edited by G. Barbera (Comitato Nazionale per le Manifestazione Celebrative, Florence, Italy, 1965).
32. C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (Freeman, New York, 1970).
33. P. Marronetti, M. Huq, P. Laguna, L. Lehner, R.A. Matzner, and D. Shoemaker, Phys. Rev. D 62, 024017 (2000).
34. P. Marronetti and R.A. Matzner, Phys. Rev. Lett. 85, 5500 (2000).
35. R. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
36. ADM in Eq. (38). For a moving source, Eq. (38) would yield γ times the result for the same source not moving (a calculation facilitated by the Kerr-Schild structure); see the discussion around Eq. (43) below. We urge the reader to carefully follow our notation.
37. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).
38. J.D. Brown and J.W. York, Phys. Rev. D 47, 1407 (1993).
39. Spatial components of angular momentum (e.g. spin) perpendicular to the motion transform with one power of γ and stay perpendicular to the motion. The orbital angular momentum L=r×p also contains one power of γ in p. Hence J contains one power of γ. See Landau and Lifshitz, Classical Theory of Fields, revised second ed. (Pergarnon, Oxford, 1962), p. 46.
40. D. Brill and R.W. Lindquist, Phys. Rev. 131, 471 (1963).
41. This was apparently first noticed as a computational result; see A. Cadez, Ann. Phys. (N.Y.) 83, 449 (1974). Čadež considered both the Brill-Lindquist [35] and Misner [37] data. For Brill-Lindquist data the apparent horizon areas are easy to compute to O(mm′/ℓ) because the lowest order effect of the distant hole on the local one is a constant, isotropic addition to the local value of the conformal factor.
42. C. Misner, Phys. Rev. 118, 1110 (1960).
43. R.H. Price and J.T. Whelan, Phys. Rev. Lett. 87, 231101 (2001).
44. Black Holes, the Membrane Paradigm, edited by K.S. Thorne, R.H. Price, and D.A. Macdonald (Yale University Press, New Haven, 1986), Sec. VIII B 1.
45. S.A. Teukolsky, Ph.D. dissertation, California Institute of Technology, 1973.
46. R. Wald, Phys. Rev. D 6, 406 (1972).
47. S. Dain, Phys. Rev. D 66, 084019 (2002).
48. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in Fortran, Second ed. (Cambridge University Press, Cambridge, 1992).
49. H. Pfeiffer, L. Kidder, M. Scheel, and S.A. Teukolsky, Comput. Phys. Commun. 152, 253 (2003).
50. P.R. Brady, J.D.E. Creighton, and K.S. Thorne, Phys. Rev. D 58, 061501(R) (1998).
51. S. Klasky, Ph.D. dissertation, University of Texas at Austin, 1966.
52. E. Schnetter, Ph.D. dissertation, University of Tübingen, 2003.
53. R.A. Matzner, talk at the conference "Gravilalion: A Decennial Perspective," Penn State University, 2003, http:// cgpg.gravily.psu.edu/ events/conferences/Gravilation_Decennial.