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The Physics of the Early Universe pp 277–298Cite as

9 Computational Black Hole Dynamics

  • Part III In Search of the Imprints of Early Universe: Gravitational Waves
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Part of the book series: Lecture Notes in Physics ((LNP,volume 653))

Abstract

Over the last decade, advances in computer hardware and numerical algorithms have opened the door to the possibility that simulations of sources of gravitational radiation can produce valuable information of direct relevance to gravitational wave astronomy. One source in particular is believed to be of extreme importance: the inspiral and merger of a binary black hole system. Simulations of binary black hole systems involve solving the Einstein equation in full generality. Such a daunting task has been one of the primary goals of the numerical relativity community. This review article focuses on the computational modelling of binary black holes. It provides a basic introduction to the subject and is intended for non-experts in the area of numerical relativity.

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References

  • 1. M. Maggiore, Gravitational Wave Experiments and Early Universe Cosmology, Phys. Reports, 331, 283 (2000).

    Google Scholar 

  • 2. T.W. Baumgarte and S.L. Shapiro. Numerical relativity and compact binaries. Phys. Reports, 376, 41 2003.

    Google Scholar 

  • 3. C. Cluter and K.S. Thorne. An overview of gravitational-wave sources. In Proceeding of GR16, 2001.

    Google Scholar 

  • 4. L. Lehner, Numerical relativity: A review, Class. Quant. Grav. 18, R25 (2001).

    Google Scholar 

  • 5. J. W. York Jr, Kinematics and dynamics of general relativity, In L. L. Smarr, editor, Sources of gravitational radiation, pages 83–126. Cambridge University Press, Cambridge, (1979).

    Google Scholar 

  • 6. R. Arnowitt, S. Deser, and C.W. Misner, The dynamics of general relativity, In L. Witten, editor, Gravitation an introduction to current research, pages 227–265. John Wiley, New York, (1962).

    Google Scholar 

  • 7. G.B. Cook, Living Rev. Rel. 5, 1 (2000).

    Google Scholar 

  • 8. G. Calabrese and O. Sarbach, J. Math. Phys. 44, 3888 (2003).

    Google Scholar 

  • 9. M. Alcubierre, Class. Quant. Grav. 20, 607 (2003).

    Google Scholar 

  • 10. M. Tiglio, L. Lehner, and D. Nilsen, gr-qc/0312001 (2003).

    Google Scholar 

  • 11. L. Lindblom, M. A. Scheel, L. E. Kidder, H. P. Pfeiffer, D. Shoemaker, and S. A. Teukolsky, gr-qc/0402027, (2004).

    Google Scholar 

  • 12. M. Anderson amd R.A. Matzner, gr-qc/0307055 (2003).

    Google Scholar 

  • 13. H. Shinkai and G. Yoneda, gr-qc/0209111, (2002).

    Google Scholar 

  • 14. O. Reula, Living Rev. Rel. 3, 1 (1998).

    Google Scholar 

  • 15. T.W. Baumgarte and S.L. Shapiro, Phys. Rev. D 59, 024007 (1999).

    Google Scholar 

  • 16. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995).

    Google Scholar 

  • 17. L.E. Kidder, M.A. Scheel, and S.A. Teukolsky, Extending the lifetime of 3d black hole computations with a new hyperbolic system of evolution equations, Phys. Rev. D64, 064017 (2001).

    Google Scholar 

  • 18. J. York, In C.R. Evans and L.S. Finn and D.W. Hobill, editors, Frontiers in Numerical Relativity, Cambridge University Press, Cambridge, (1989).

    Google Scholar 

  • 19. J. Thornburg, A fast apparent-horizon finder for 3-dimensional cartesian grids in numerical relativity, Class. Quant. Grav. 21, 743 (2004).

    Google Scholar 

  • 20. M. Alcubierre, B. Brügmann, P. Diener, M. Koppitz, D. Pollney, E. Seidel, and R. Takahashi, Gauge conditions for long-term numerical black hole evolutions without excision, Phys. Rev. D67, 084023 (2003).

    Google Scholar 

  • 21. G.B. Cook and BBH Alliance, Boosted three-dimensional black hole evolutions with singularity excision, Phys. Rev. Lett. 80, 2512 (1998).

    Google Scholar 

  • 22. S. Brandt, R. Correll, R. Gómez, M. Huq, P. Laguna L. Lehner, D. Neilsen, R. Matzner, J. Pullin, E. Schnetter, D. Shoemaker, and J. Winicour, Grazing collisions of black holes via the excision of singularities, Phys. Rev. Lett. 85, 5496 (2000).

    Google Scholar 

  • 23. R. Gómez, L. Lehner, R. Marsa, and J. Winicour, Moving black holes in 3d, Phys. Rev. D57, 4778 (1998).

    Google Scholar 

  • 24. E. Seidel and W. Suen, Phys. Rev. Lett. 69, 1845 (1992).

    Google Scholar 

  • 25. P. Anninos, G. Gaues, J. Masso, E. Seidel, and L. Smarr, Horizon boundary condition for black hole spacetimes, Phys. Rev. D51, 5562 (1995).

    Google Scholar 

  • 26. R. Marsa and M. Choptuik, Black hole–scalar field interactions in spherical symmetry, Phys. Rev. D54, 4929 (1996).

    Google Scholar 

  • 27. M. Scheel, T. Baumgarte, G. Cook, S. Shapiro, and S. Teukolsky, Numerical evolution of black holes with a hyperbolic formulation of general relativity, Phys. Rev. D56, 6320 (1997).

    Google Scholar 

  • 28. M. Alcubierre and B. Brügmann, Simple excision of a black hole in 3+1 numerical relativity, Phys. Rev. D63, 104006 (2001).

    Google Scholar 

  • 29. H. Yo, T. Baumgarte, and S. Shapiro, A numerical testbed for singularity excision in moving black hole spacetimes, Phys. Rev. D64, 124011 (2001).

    Google Scholar 

  • 30. D. Shoemaker, K. Smith, U. Sperhake, P. Laguna, E. Schnetter, and D. Fiske, Class. Quant. Grav. 20, 3729 (2003).

    Google Scholar 

  • 31. U. Sperhake, K. Smith, B. Kelly, P. Laguna, and D. Shoemaker, Phys. Rev. D69, 024012 (2004).

    Google Scholar 

  • 32. G. Calabrese, L. Lehner, D. Neilsen, J. Pullin, O. Reula, O. Sarbach, and M. Tiglio, Novel finite-differencing techniques for numerical relativity: application to black hole excision, Class. Quant. Grav. 20, L245 (2003).

    Google Scholar 

  • 33. A. Ashtekar, C. Beetle, and S. Fairhurst, Mechanics of isolated horizons, Class. Quant. Grav. 17, 253 (2000).

    Google Scholar 

  • 34. A. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Krishnan, J. Lewandowski, and J. Wisniewski, Generic isolated horizons and their applications, Phys. Rev. Lett. 85, 3564 (2000).

    Google Scholar 

  • 35. A. Ashtekar and B. Krishnan, Dynamical horizons: Energy, angular momentum, fluxes and balance laws, Phys. Rev. Lett. 89, 261101 (2002).

    Google Scholar 

  • 36. A. Ashtekar and B. Krishnan, Dynamical horizons and their properties, Phys. Rev. D68, 104030 (2003).

    Google Scholar 

  • 37. O. Dreyer, B. Krishnan, E. Schnetter, and D. Shoemaker, Introduction to isolated horizons in numerical relativity, Phys. Rev. D67, 024018 (2003).

    Google Scholar 

  • 38. A. Ashtekar, S. Fairhurst, and B. Krishnan, Isolated horizons: Hamiltonian evolution and the first law, Phys. Rev. D62, 104025 (2000).

    Google Scholar 

  • 39. A. Ashtekar, C. Beetle, and J. Lewandowski, Mechanics of rotating isolated horizons, Phys. Rev. D64, 044016 (2001).

    Google Scholar 

  • 40. S. Brandt and B. Brügmann, A simple construction of initial data for multiple black holes, Phys. Rev. Lett. 78, 3606 (1997).

    Google Scholar 

  • 41. C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation. Freeman: San Francisco, (1973).

    Google Scholar 

  • 42. R.A. Matzner, M.F. Huq, and D. Shoemaker, Initial data and coordinates for multiple black hole systems, Phys. Rev. D59, 024015 (1999).

    Google Scholar 

  • 43. Harald P. Pfeiffer and Gregory B. Cook and Saul A. Teukolsky, Comparing initial-data sets for binary black holes, Phys. Rev. D66, 024047 (2002).

    Google Scholar 

  • 44. P. Anninos, K. Camarda J. Massó, E. Seidel, W. Suen, and J. Towns, Three dimensional numerical relativity: the evolution of black holes, Phys. Rev. D52, 2059 (1995).

    Google Scholar 

  • 45. R. Gómez et al, Stable characteristic evolution of generic three-dimensional single black hole space-times, Phys. Rev. Lett. 80, 3915 (1998).

    Google Scholar 

  • 46. M. Alcubierre, B. Brügmann, D. Pollney, E. Seidel, and R. Takahashi, Black hole excision for dynamic black holes, Phys. Rev. D64, 061501 2001.

    Google Scholar 

  • 47. H.-J. Yo, T. W. Baumgarte, and S. L. Shapiro, Phys. Rev. D66, 084026 (2002).

    Google Scholar 

  • 48. S. Brandt, K. Camarda, E. Seidel, and R. Takahashi, Three dimensional distorted black holes, Class. Quant. Grav. 20, 1 (2003).

    Google Scholar 

  • 49. R. Gómez, Gravitational waveforms with controlled accuracy, Phys. Rev. D64, 024007 (2001).

    Google Scholar 

  • 50. J. Baker, S. Brandt, M. Campanelli, C. Lousto, E. Seidel, and R. Takahashi, Nonlinear and perturbative evolution of distorted black holes. ii. odd-parity modes, Phys. Rev. D62, 127701 (2000).

    Google Scholar 

  • 51. G. Allen, K. Camarda, and E. Seidel, Black hole spectroscopy: Determining waveforms from 3d excited black holes, gr-qc/9806036 (1998).

    Google Scholar 

  • 52. D.R. Briland and R.W. Lindquist, Phys. Rev. 131, 471 (1963).

    Google Scholar 

  • 53. P. Papadopoulos, Nonlinear harmonic generation in finite amplitude black hole oscillations, Phys. Rev. D65, 084016 2002.

    Google Scholar 

  • 54. Y. Zlochower, R Gómez, S. Husa, L. Lehner, and J. Winicour, Mode coupling in the nonlinear response of black holes, Phys. Rev. D68, 084014 (2003).

    Google Scholar 

  • 55. S. Hahn and R. Lindquist, The two body problem in geometrodynamics, Annals of Physics 29, 304 (1964).

    Google Scholar 

  • 56. L. L. Smarr, Gauge conditions, radiation formulae and the two black hole collisions, In L. L. Smarr, editor, Sources of gravitational radiation, page 275. Cambridge University Press, Cambridge, (1979).

    Google Scholar 

  • 57. B. Brügmann, Binary black hole mergers in 3d numerical relativity, Int. J. Mod. Phys. D8, 85 (1999).

    Google Scholar 

  • 58. P. Marronetti, M. Huq, P. Laguna, L. Lehner, R. Matzner, and D. Shoemaker, Approximate analytical solutions to the initial data problem of black hole binary systems, Phys. Rev. D62, 024017 (2000).

    Google Scholar 

  • 59. M. Alcubierre, W. Benger, B. Brügmann, G. Lanfermann, L. Nerger, E. Seidel, and R. Takahashi, The 3d grazing collision of two black holes, Phys. Rev. Lett. 87, 271103 (2001).

    Google Scholar 

  • 60. J. Baker, M. Campanelli, C.O. Lousto, and R. Takahashi, The lazarus project: A pragmatic approach to binary black hole evolutions, Phys. Rev. D 65, 124012 (2002).

    Google Scholar 

  • 61. J. Baker, B. Brügmann, M. Campanelli, and C.O. Lousto, Gravitational waves from black hole collisions via an eclectic approach, Class. Quant. Grav. 17, L149 (2000).

    Google Scholar 

  • 62. J. Baker, B. Brügmann, M. Campanelli, C.O. Lousto, and R. Takahashi, Plunge waveforms from inspiralling binary black holes, Phys. Rev. Lett. 87, 121103 (2001).

    Google Scholar 

  • 63. B. Brügmann, W. Tichy, and N. Jansen, Numerical simulation of orbiting black holes, gr-qc/0312112 (2003).

    Google Scholar 

  • 64. E. Schnetter, S. Hawley, and I. Hawke, Evolutions in 3d numerical relativity using fixed mesh refinement, Class. Quant. Grav 21, 1465 (2004).

    Google Scholar 

  • 65. B. Imbiriba, J. Baker, D. Choi, J. Centrella, D. Fiske, J. Brown, J. van Meter, and K. Olson, Evolving a puncture black hole with fixed mesh refinement, gr-qc/0403048 (2004).

    Google Scholar 

  • 66. L. Kidder, M. Scheel, S. Teukolsky, E. Carlson, and G. Cook, Black hole evolution by spectral methods, Phys. Rev. D62, 084032 (2000).

    Google Scholar 

  • 67. S. Bonazzola, E. Gourgoulhon, and J. Marck, Spectral methods in general relativistic astrophysics, J. Comput. Appl. Math. 109, 892 (1999).

    Google Scholar 

  • 68. P. Grandclément, S. Bonazzola, E. Gourgoulhon, and J. Marck, A multi-domain spectral method for scalar and vectorial poisson equations with non-compact sources, J. Comput. Phys. 170, 231 (2001).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Astronomy and Astrophysics, Institute for Gravitational Physics and Geometry, Center for Gravitational Wave Physics, Penn State University, University Park, PA 16802, USA

    Pablo Laguna

  2. Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA

    Deirdre M. Shoemaker

Authors
  1. Pablo Laguna
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  2. Deirdre M. Shoemaker
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E. Papantonopoulos

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Laguna, P., Shoemaker, D.M. 9 Computational Black Hole Dynamics. In: Papantonopoulos, E. (eds) The Physics of the Early Universe. Lecture Notes in Physics, vol 653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31535-3_9

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  • DOI: https://doi.org/10.1007/978-3-540-31535-3_9

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