Skip to main content

Colliding Black Holes and Gravitational Waves

  • Chapter
Physics of Black Holes

Part of the book series: Lecture Notes in Physics ((LNP,volume 769))

Abstract

This article presents a summary of numerical simulations of black-hole spacetimes in the framework of general relativity. The first part deals with the 3+1 decomposition of generic spacetimes as well as the Einstein equations which forms the basis of most work in numerical relativity. Technical aspects of the resulting numerical evolutions and the diagnostics of the resulting spacetimes are discussed. The second part presents an overview of the history of numerical simulations of black-hole spacetimes. Finally, we summarize results derived from numerical black-hole simulations obtained after the breakthrough in 2005. The relevance of these results in the context of astrophysics, gravitational wave physics, and fundamental physics is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. B. Abbott and the LIGO Scientific Collaboration, LIGO: The Laser Interferometer Gravitational-Wave Observatory. (2007) arXiv:0711.3041 [gr-qc].

    Google Scholar 

  2. A. M. Abrahams and C. R. Evans, Gauge-invariant treatment of gravitational radiation near the source: Analysis and numerical simulations. Phys. Rev. D 42, 2585 (1990).

    Article  ADS  Google Scholar 

  3. A. M. Abrahams, D. Bernstein, D. Hobill, E. Seidel and L. Smarr, Numerically generated black-hole spacetimes: {I}nteraction with gravitational waves. Phys. Rev. D 45, 3544 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  4. F. Acernese and the VIRGO Collaboration, Status of VIRGO. Class. Quant. Grav. 22, S869 (2005).

    Article  ADS  Google Scholar 

  5. P. Ajith et al., Phenomenological template family for black-hole coalescence waveforms. Class. Quant. Grav. 24 S689 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. P. Ajith et al., A template bank for gravitational waveforms from coalescing binary black holes: I. non-spinning binaries. arXiv:0710.2335 (2007).

    Google Scholar 

  7. M. Alcubierre and B. Brügmann, Simple excision of a black hole in 3+1 numerical relativity. Phys. Rev. D. 63, 104006 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  8. M. Alcubierre et al., The 3{D} grazing collision of two black holes. Phys. Rev. Lett. 87, 271103 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Alcubierre et al., Gauge conditions for long-term numerical black hole evolutions without excision. Phys. Rev. D. 67, 084023 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  10. M. Alcubierre, Hyperbolic slicings of spacetime: Singularity avoidance and gauge shocks. Class. Quant. Grav. 20, 607 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. M. Alcubierre et al., Dynamical evolution of quasi-circular binary black hole data. Phys. Rev. D. 72, 044004 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Alcubierre, Are gauge shocks really shocks? aClass. Quant. Grav. 22, 4071 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. A. Anderson and J. W. York Jr., Fixing Einstein’s Equations. Phys. Rev. Lett. 82, 4384 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. M. Anderson et al., Simulating binary neutron stars: Dynamics and gravitational waves. arXiv:0708.2720 [gr-qc]. (2007).

    Google Scholar 

  15. M. Ando and the TAMA Collaboration, Current status of the TAMA300 gravitational wave detector. Class. Quant. Grav. 22, S881 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  16. P. Anninos, D. Hobill, E. Seidel, L. Smarr and W.-M. Suen, Collision of two black holes. Phys. Rev. Lett. 71, 2851 (1993).

    Article  ADS  Google Scholar 

  17. P. Anninos, G. Daues, J. Massó, E. Seidel and W.-M. Suen, Horizon boundary condition for black hole spacetimes. Phys. Rev. D. 51, 5562 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  18. P. Anninos, K. Camarda, J. Massó, E. Seidel and W.-M. Suen, Three-dimensional numerical relativity: The evolution of black holes. Phys. Rev. D. 52, 2059 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  19. P. Anninos, D. Hobill, E. Seidel, L. Smarr and W.-M. Suen, Head-on collision of two equal mass black holes. Phys. Rev. D. 52, 2044 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  20. P. Anninos, R. H. Price, J. Pullin, E. Seidel and W.-M. Suen, Head-on collision of two black holes: Comparison of different approaches. Phys. Rev. D. 52, 4462 (1995).

    Article  ADS  Google Scholar 

  21. P. Anninos and S. Brandt, Head-on collision of two unequal mass black holes. Phys. Rev. Lett. 81, 508 (1998).

    Article  ADS  Google Scholar 

  22. P. Anninos, K. Camarda, J. Libson, J. Massó, E. Seidel and W.-M. Suen, Finding apparent horizons in dynamic 3{D} numerical spacetimes. Phys. Rev. D. 58, 024003 (1998).

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Ansorg, Multi-domain spectral method for initial data of arbitrary binaries in general relativity. Class. Quant. Grav. 24, S1 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. T. Apostolatos, Search templates for gravitational waves from precessing, inspiralling binaries. Phys. Rev. D 52 605 (1995).

    Article  ADS  Google Scholar 

  25. R. Arnowitt, S. Deser and C. W. Misner, (1962). The dynamics of general relativity. In L. Witten (Ed.), Gravitation an Introduction to Current Research (pp. 227–265). New York: John Wiley. gr-qc/0405109.

    Google Scholar 

  26. K. G. Arun, B. R. Iyer, B. S. Sathyaprakash and S. Sinha, Higher harmonics increase {LISA}’s mass reach for supermassive black holes. Phys. Rev. D 75 124002 (2007).

    Article  ADS  Google Scholar 

  27. K. G. Arun, B. R. Iyer, B. S. Sathyaprakash, S. Sinha and C. Van Den Broek, Higher signal harmonics, LISA’s angular resolution and dark energy. Phys. Rev. D 76 104016 (2007).

    Article  ADS  Google Scholar 

  28. A. Ashtekar and B. Brishnan, Isolated and dynamical horizons and their applications. Living Rev. Relativity 2004-10 url: http://relativity.livingreviews.org/Articles/lrr-2004-10/download/index.html. Cited 29 Jan 2008.

  29. J. G. Baker et al., Collision of boosted black holes. Phys. Rev. D 55, 829 (1997).

    Article  ADS  Google Scholar 

  30. J. G. Baker, B. Brügmann and M. Campanelli, Gravitational waves from black hole collisions via an eclectic approach. Class. Quant. Grav. 17, L149 (2000).

    Article  MATH  ADS  Google Scholar 

  31. J. G. Baker, M. Campanelli, C. O. Lousto and R. Takahashi, Modeling gravitational radiation from coalescing binary black holes. Phys. Rev. D 65, 124012 (2002).

    Article  ADS  Google Scholar 

  32. J. Baker, M. Campanelli and C. O. Lousto, The Lazarus project: A pragmatic approach to binary black hole evolutions. Phys. Rev. D. 65 044001 (2002).

    Article  ADS  Google Scholar 

  33. J. G. Baker, M. Campanelli, C. O. Lousto and R. Takahashi, The coalescence remnant of spinning binaries. Phys. Rev. D 69, 027505 (2004).

    Article  ADS  Google Scholar 

  34. J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz, and J. van Meter, Gravitational-wave extraction from an inspiraling configuration+ of merging black holes. Phys. Rev. Lett. 96, 111102 (2006).

    Article  ADS  Google Scholar 

  35. J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz and J. van Meter, Binary black hole merger dynamics and waveforms. Phys. Rev. D 73, 104002 (2006).

    Article  ADS  Google Scholar 

  36. J. G. Baker et al., Getting a kick out of numerical relativity. Astrophys. J. 653 L93 (2006).

    Article  ADS  Google Scholar 

  37. J. G. Baker, J. R. van Meter, S. T. McWilliams, J. Centrella and B. J. Kelly, Consistency of post-Newtonian waveforms with numerical relativity. Phys. Rev. Lett. 99, 181101 (2007).

    Article  ADS  Google Scholar 

  38. J. G. Baker et al., Binary black hole late inspiral: Simulations for gravitational wave observations. Phys. Rev. D 75, 124024 (2007).

    Article  ADS  Google Scholar 

  39. J. G. Baker, M. Campanelli, F. Pretorius and Y. Zlochower, Comparisons of binary black hole merger waveforms. Class. Quant. Grav. 24, S25 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. J. G. Baker et al., Modeling kicks from the merger of generic black-hole binaries. (2005), arXiv:0802.0416 [astro-ph].

    Google Scholar 

  41. J. Balakrishna, G. Daues, E. Seidel, W.-M. Suen, M. Tobias and E. Wang, Coordinate conditions in three-dimensional numerical relativity. Class. Quant. Grav. 13 L135 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  42. T. W. Baumgarte, G. B. Cook, M. A. Scheel, S. L. Shapiro and S. A. Teukolsky, Implementing an apparent-horizon finder in three dimensions. Phys. Rev. D 54 4849 (1996).

    Article  ADS  Google Scholar 

  43. T. W. Baumgarte and S. L. Shapiro, On the numerical integration of Einstein’s field equations. Phys. Rev. D 59 024007 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  44. T. W. Baumgarte, Innermost stable circular orbit of binary black holes. Phys. Rev. D 62 024018 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  45. T. W. Baumgarte and S. L. Shapiro, Numerical relativity and compact binaries. Phys. Rept. 376 41 (2003).

    Google Scholar 

  46. T. Baumgarte, P. Brady, J. D. E. Creighton, L. Lehner, F. Pretorius and R. De Voe, Learning about compact binary merger: The interplay between numerical relativity and gravitational-wave astronomy (2006), gr-qc/0612100.

    Google Scholar 

  47. F. Acernese et al., A comparison of methods for gravitational wave burst searches from {LIGO} and {Virgo}. (2007) gr-qc/0701026.

    Google Scholar 

  48. C. Beetle, M. Bruni, L. M. Burko and A. Nerozzi, Towards a novel wave-extraction method for numerical relativity. I. Foundations and initial-value formulation. Phys. Rev. D. 72 024013 (2005).

    Article  ADS  Google Scholar 

  49. J. D. Bekenstein, Gravitational-radiation recoil and runaway black holes. Astrophys. J. 183 657 (1973).

    Article  ADS  Google Scholar 

  50. M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53 484 (1984).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  51. E. Berti and V. Cardoso, Quasinormal ringing of Kerr black holes. I: The excitation factors. Phys. Rev. D 74 104020 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  52. E. Berti et al., Inspiral, merger and ringdown of unequal mass black hole binaries: A multipolar analysis. Phys. Rev. D 76 064034 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  53. E. Berti, V. Cardoso, J. A. González, U. Sperhake and B. Brügmann, Multipolar analysis of spinning binaries. (2007) arXiv:0711.1097 [gr-qc].

    Google Scholar 

  54. L. Blanchet, Innermost circular orbit of binary black holes at the third post-Newtonian approximation. Phys. Rev. D 65 124009 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  55. L. Blanchet, M. S. S. Qusailah and C. M. Will, Gravitational recoil of sinpiralling black hole binaries to second post-Newtonian order. Astrophys. J. 635 508 (2005).

    Article  ADS  Google Scholar 

  56. L. Blanchet, Gravitational radiation from post-newtonian sources and inspiralling compact binaries. Living Rev. Relativity 2006-4 url: http://www.livingreviews.org/Articles/lrr-2006-4/download/index.html. Cited 29 Jan 2008.

  57. T. Bode, D. Shoemaker, F. Herrmann and I. Hinder, Delicacy of Binary Black Hole Mergers in the Presence of Spurious Radiation. (2007) arXiv:0711.0669 [gr-qc].

    Google Scholar 

  58. T. Bogdanovic, C. S. Reynolds and M. C. Miller, Alignment of the spins of supermassive black holes prior to coalescence (2007), astro-ph/0703054.

    Google Scholar 

  59. C. Bona and J. Massó, Hyperbolic evolution systems for numerical relativity. Phys. Rev. Lett. 68, 1097 (1992).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. C. Bona, J. Massó, E. Seidel and J. Stela, A new formalism for numerical relativity. Phys. Rev. Lett. 75, 600 (1995).

    Article  ADS  Google Scholar 

  61. C. Bona, J. Massó, E. Seidel and J. Stela, First order hyperbolic formalism for numerical relativity. Phys. Rev. D 56, 3405 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  62. C. Bona, T. Ledvinka and C. Palenzuela, General-covariant evolution formalism for numerical relativity. Phys. Rev. D. 67 104005 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  63. E. W. Bonning, G. A. Shields and S. Salviander, Recoiling Black Holes in Quasars (2005) arXiv:0705.4263 [astro-ph].

    Google Scholar 

  64. I. Booth, Black hole boundaries. Can. J. Phys. 83, 1073 (2005).

    Article  ADS  Google Scholar 

  65. M. Boylan-Kolchin, C.-P. Ma and E. Quataert, Core formation in Galactic nuclei due to recoiling black holes. Astrophys. J. 613, L37 (2004).

    Article  ADS  Google Scholar 

  66. H. Bondi, M. G. J. van der Burg and R. A. Metzner, Gravitational waves in general relativity {VII}. Waves from axi-symmetric isolated systems. Proc. Roy. Soc. A. 269, 21 (1962).

    Article  MATH  ADS  Google Scholar 

  67. E. Bonning, P. Marronetti, D. Neilsen and R. A. Matzner, Physics and initial data for multiple black hole spacetimes. Phys. Rev. D. 68, 044019 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  68. W. B. Bonnor and M. A. Rotenberg, Transport of momentum by gravitational waves: The linear approximation. Proc. Roy. Soc. A 265, 109 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  69. J. M. Bowen and J. W. York Jr., Time-asymmetric initial data for black holes and black-hole collisions. Phys. Rev. D. 21, 2047 (1980).

    Article  ADS  Google Scholar 

  70. M. Boyle et al., High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions. (2007) arXiv:0710.0158 [gr-qc].

    Google Scholar 

  71. L. Boyle, M. Kesden and S. Nissanke, Binary black hole merger: Symmetry and the spin expansion. (2007) arXiv:0709.0299 [gr-qc].

    Google Scholar 

  72. L. Boyle and M. Kesden, The spin expansion for binary black hole merger: New predictions and future directions. (2007) arXiv:0712.2819 [astro-ph].

    Google Scholar 

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

    Article  ADS  Google Scholar 

  74. S. Brandt et al., Grazing collisions of black holes via the excision of singularities. Phys. Rev. Lett. 85, 5496 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  75. D. R. Brill and R. W. Lindquist, Interaction energy in geometrostatics. Phys. Rev. 131, 471 (1963).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  76. D. Brown et al., Searching for gravitational waves from binary inspiral with LIGO. Class. Quant. Grav. 21, S1625 (2004).

    Article  MATH  ADS  Google Scholar 

  77. J. D. Brown, Puncture Evolution of Schwarzschild Black Holes. (2007) arXiv:0705.1359 [gr-qc].

    Google Scholar 

  78. B. Brügmann, Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions. Phys. Rev. D 54, 7361 (1996).

    Article  ADS  Google Scholar 

  79. B. Brügmann, Binary black hole mergers in 3D numerical relativity. Int. J. Mod. Phys. 8, 85 (1999).

    MATH  ADS  Google Scholar 

  80. B. Brügmann, W. Tichy and N. Jansen, Numerical simulation of orbiting black holes. Phys. Rev. Lett. 92, 211101 (2004).

    Article  ADS  Google Scholar 

  81. B. Brügmann et al., Calibration of moving puncture simulations. Phys. Rev. D. 77, 024027 (2008).

    Article  ADS  Google Scholar 

  82. B. Brügmann, J. A. González, M. D. Hannam, S. Husa and U. Sperhake, Exploring black hole superkicks. (2007) arXiv:0707.0135 [gr-qc].

    Google Scholar 

  83. Y. Bruhat, The Cauchy problem. In L. Witten (Ed.), Gravitation: An Introduction to Current Research. (Cambirdge University Press, Cambridge, 1962).

    Google Scholar 

  84. A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics. Phys. Rev. D 59 084006 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  85. A. Buonanno, Y. Chen and M. Valisneri, Detection template families for gravitational waves from the final stages of binary-black-hole inspirals: Nonspinning case. Phys. Rev. D 67 024016 (2003).

    Article  ADS  Google Scholar 

  86. A. Buonanno, G. B. Cook and F. Pretorius, Inspiral, merger and ring-down of equal-mass black-hole binaries. Phys. Rev. D. 75, 124018 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  87. A. Buonanno, L. Kidder and L. Lehner, Estimating the final spin of a binary black hole coalescence. Phys. Rev. D. 77 026004 (2008).

    Article  ADS  Google Scholar 

  88. A. Buonanno et al., Toward faithful templates for non-spinning binary black holes using the effective-one-body approach. Phys. Rev. D 76 104049 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  89. {Cactus Computational Toolkit homepage}. url: http://www.cactuscode.org/. Cited 29 Jan 2008.

  90. G. Calabrese, J. Pullin, O. Sarbach and M. Tiglio, Convergence and stability in numerical relativity. Phys. Rev. D. 66, 041501 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  91. G. Calabrese, J. Pullin, O. Sarbach, M. Tiglio and O. Reula, Well posed constraint-preserving boundary conditions for the linearized Einstein equations. Commun. Math. Phys. 240, 377 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  92. M. Campanelli and C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole. Phys. Rev. D 59, 124022 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  93. M. Campanelli, Understanding the fate of merging supermassive black holes. Class. Quant. Grav. 22, S387 (2005).

    Article  MATH  ADS  Google Scholar 

  94. M. Campanelli, C. O. Lousto, P. Marronetti and Y. Zlochower, Accurate evolutions of orbiting black-hole binaries without excision. Phys. Rev. Lett. 96, 111101 (2006).

    Article  ADS  Google Scholar 

  95. M. Campanelli, C. O. Lousto and Y. Zlochower, Last orbit of binary black holes. Phys. Rev. D 73, 061501 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  96. M. Campanelli, C. O. Lousto and Y. Zlochower, Gravitational radiation from spinning-black-hole binaries: The orbital hang up. Phys. Rev. D 74, 041501 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  97. M. Campanelli, C. O. Lousto and Y. Zlochower, Spin-orbit interactions in black-hole binaries. Phys. Rev. D 74, 084023 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  98. M. Campanelli, C. O. Lousto, Y. Zlochower, B. Krishnan and D. Merritt, Spin flips and precession in black-hole-binary mergers. Phys. Rev. D 75 064030 (2007).

    Google Scholar 

  99. M. Campanelli, C. O. Lousto and Y. Zlochower, Large merger recoils and spin flips from generic black-hole binaries. Astrophys. J. 659, L5 (2007).

    Article  ADS  Google Scholar 

  100. M. Campanelli, C. O. Lousto, Y. Zlochower and D. Merritt, Maximum gravitational recoil. Phys. Rev. Lett. 98, 231102 (2007).

    Article  ADS  Google Scholar 

  101. Carpet Code homepage. url: http://www.carpetcode.org/. Cited 29 Jan 2008}.

  102. S. Chadrasekhar and S. Detweiler, The quasi-normal modes of the Schwarzschild black hole. Proc. Roy. Soc. A 344 441 (1975).

    Article  ADS  Google Scholar 

  103. D.-I. iChoi et al., Recoiling from a kick in the head-on collision of spinning black holes. Phys. Rev. D 76 104026 (2007).

    Article  ADS  Google Scholar 

  104. M. W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field. Phys. Rev. Lett. 70, 9 (1993).

    Article  ADS  Google Scholar 

  105. D. Christodoulou, Reversible and irreversible transformations in black hole physics. Phys. Rev. Lett. 25, 1596 (1970).

    Article  ADS  Google Scholar 

  106. G. B. Cook, Three-dimensional initial data for the collision of two black holes. II. Quasicircular orbits for equal-mass black holes. Phys. Rev. D 50, 5025-5032 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  107. G. B. Cook, Initial data for numerical relativity. Living Rev. Relativity 2000-5 url: http://relativity.livingreviews.org/Articles/lrr-2000-5/download/index.html. Cited 29 Jan 2008}.

  108. G. B. Cook, Corotating and irrotational binary black holes in quasicircular orbits. Phys. Rev. D 65, 084003 (2002).

    Article  ADS  Google Scholar 

  109. G. B. Cook and H. Pfeiffer, Excision boundary conditions for black hole initial data. Phys. Rev. D 70, 104016 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  110. S. Dain, J. L. Jaramillo and B. Krishnan, On the existence of initial data containing isolated black holes. Phys. Rev. D 71, 064003 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  111. T. Damour, P. Jaranowski and G. Schäfer, Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation. Phys. Rev. D 62 084011 (2000).

    Article  ADS  Google Scholar 

  112. T. Damour, P. Jaranowski and G. Schäfer, Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation. Phys. Rev. D 62, 044024 (2000).

    Article  ADS  Google Scholar 

  113. T. Damour, E. Gourgoulhon and P. Grandclément, Circular orbits of corotating binary black holes: Comparison between analytical and numerical results. Phys. Rev. D 66 024007 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  114. T. Damour and A. Gopakumar, Gravitational recoil during binary black hole coalescence using the effective one body approach. Phys. Rev. D 73 124006 (2006).

    Article  ADS  Google Scholar 

  115. T. Damour and A. Nagar, Final spin of a coalescing black-hole binary: An effective-one-body approach. Phys. Rev. D 76 044003 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  116. P. Diener et al., Accurate evolution of orbiting binary black holes. Phys. Rev. Lett. 96, 121101 (2006).

    Article  ADS  Google Scholar 

  117. O. Dreyer, B. Krishnan, E. Schnetter and D. Shoemaker, Introduction to isolated horizons in numerical relativity. Phys. Rev. D 67, 024018 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  118. G. Efstathiou and M. Rees, High-redshift quasars in the Cold Dark Matter cosmogony. MNRAS 230, 5 (1988).

    ADS  Google Scholar 

  119. K. R. Eppley (1975). The numerical evolution of the collision of two black holes Phd Thesis, Princeton University.

    Google Scholar 

  120. Z. Etienne, J. A. Faber, Y. T. Liu, S. L. Shapiro, K. Taniguchi and T. Baumgarte, Fully general relativistic simulations of black-hole-neutron star mergers. (2007) arXiv:0712.2460 [astro-ph].

    Google Scholar 

  121. X. Fan et al., A survey of $z>5.7$ Quasars in the sloan digital sky survey. II. Discovery of three additional quasars at $z>6$. Astron. J. 125, 1649 (2003).

    Article  ADS  Google Scholar 

  122. M. Favata, S. A. Hughes and D. E. Holz, How black holes get their kicks: {G}ravitational radiation recoil revisited. Astrophys. J. 607, L5 (2004).

    Article  ADS  Google Scholar 

  123. L. Ferrares and D. Merritt, A fundamental relation between supermassive black holes and their host galaxies. Astrophys. J. 539, L9 (2000).

    Article  ADS  Google Scholar 

  124. L. Ferrarese and H. Ford, Supermassive black holes in galactic nuclei: Past, present and future research. Sp. Sci. Rev. 116 523 (2005).

    Article  ADS  Google Scholar 

  125. D. R. Fiske, Wave zone extraction of gravitational radiation in three-dimensional numerical relativity. Phys. Rev. D. 71, 104036 (2005).

    Article  ADS  Google Scholar 

  126. M. J. Fitchett, The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system. MNRAS. 203 1049 (1983).

    MATH  ADS  Google Scholar 

  127. M. J. Fitchett and S. Detweiler, Linear momentum and gravitational waves - Circular orbits around a Schwarzschild black hole. MNRAS. 211 933 (1984).

    ADS  Google Scholar 

  128. J. Frauendiener, Conformal Infinity. Living Rev. Relativity 2004-1 url: http:// relativity.livingreviews.org/Articles/lrr-2004-1/download/index.html. Cited 19 Feb 2008}.

  129. H. Friedrich, Cauchy problems for the conformal vacuum field equations in general relativity. Comm. Math. Phys. 91, 445 (1983).

    Google Scholar 

  130. H. Friedrich, Hyperbolic reductions for Einstein’s equations. Class. Quant. Grav. 13, 1451 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  131. H. Friedrich and G. Nagy, The initial boundary value problem for Einstein’s vacuum field equations. Commun. Math. Phys. 201, 619 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  132. S. Frittelli and R. Gomez, Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations. Phys. Rev. D 69, 124020 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  133. A. Garat and R. H. Price, Nonexistence of conformally flat slices of the Kerr spacetime. Phys. Rev. D 61, 124011 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  134. D. Garfinkle, Harmonic coordinate method for simulating generic singularities. Phys. Rev. D. 65, 044029 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  135. K. Gebhardt et al., A relationship between nuclear black hole mass and galaxy velocity dispersion. Astrophys. J. 539, L13 (2000).

    Article  ADS  Google Scholar 

  136. J. A. González, U. Sperhake, B. Brügmann, M. D. Hannam and S. Husa, The maximum kick from nonspinning black-hole binary inspiral. Phys. Rev. Lett. 98 091101 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  137. J. A. González, M. D. Hannam, U. Sperhake, B. Brügmann and S. Husa, Supermassive kicks for spinning black holes. Phys. Rev. Lett. 98 231101 (2007).

    Article  ADS  Google Scholar 

  138. E. Gourgoulhon, P. Grandclément and S. Bonazzola, Binary black holes in circular orbits. I. A global spacetime approach. Phys. Rev. D 65, 044020 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  139. E. Gourgoulhon and J. L. Jaramillo, A 3+1 perspective on null hypersurfaces and isolated horizons. Phys. Rept. 423, 159 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  140. E. Gourgoulhon, 3+1 {F}ormalism and bases of numerical relativity. (2000) gr-qc/0703035.

    Google Scholar 

  141. P. Grandclément, E. Gourgoulhon and S. Bonazzola, Binary black holes in circular orbits. II. Numerical methods and first results. Phys. Rev. D 65, 044021 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  142. A. Gualandris and D. Merritt, Ejection of supermassive black holes from galaxy cores. (2007) arXiv:0708.0771 [astro-ph].

    Google Scholar 

  143. C. Gundlach and J. M. Martín-García, Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations. Phys. Rev. D 70, 044032 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  144. C. Gundlach, G. Calabrese, I. Hinder and J. M. Martín-García, Constraint damping in the {Z}4 formulation and harmonic gauge. Class. Quant. Grav. 22, 3767 (2005).

    Article  MATH  Google Scholar 

  145. C. Gundlach and J. M. Martín-García, Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints. Phys. Rev. D. 70, 044031 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  146. C. Gundlach and J. M. Martín-García, Critical phenomena in gravitational collapse. Living Rev. Relativity 2007-5 url: http://relativity.livingreviews.org/Articles/lrr-2007-5/download/index.html. Cited 29 Jan 2008}.

  147. HAD homepage. url: http://had.liu.edu/. Cited 29 Jan 2008.

  148. M. G. Haehnelt, M. B. Davies and M. J. Rees, Possible evidence for the ejection of a supermassive black hole from an ongoing merger of galaxies. MNRAS 366, L22 (2005).

    Google Scholar 

  149. S. G. Hah and R. W. Lindquist, The two body problem in geometrodynamics. Ann. Phys. 29, 304 (1964).

    Article  ADS  Google Scholar 

  150. Z. Haiman and A. Loeb, What is the highest plausible redshift of luminous quasars? Astrophys. J. 552, 459 (2001).

    Article  ADS  Google Scholar 

  151. Z. Haiman, Constraints from gravitational recoil on the growth of supermassive black holes at high redshift. Astrophys. J. 613, 36 (2004).

    Article  ADS  Google Scholar 

  152. M. D. Hannam, S. Husa, D. Pollney, B. Brügmann and N. Ó Murchadha, Geometry and regularity of moving punctures. Phys. Rev. Lett. 99, 241102 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  153. M. D. Hannam et al., Where post-Newtonian and numerical-relativity waveforms meet. (2007) arXiv:0706.1305 [gr-qc].

    Google Scholar 

  154. M. D. Hannam, S. Husa, B. Brügmann and A. Gopakumar, Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: The orbital hang-up case. (2007) arXiv:0712.3787 [gr-qc].

    Google Scholar 

  155. G. Heinzel et al., {LISA} interferometry: Recent developments. Class. Quant. Grav. 23, S119 (2006).

    Article  ADS  Google Scholar 

  156. F. Herrmann, I. Hinder, D. Shoemaker and P. Laguna, Unequal-mass binary black hole plunges and gravitational recoil. Class. Quant. Grav. 24, S33 (2007).

    MATH  MathSciNet  Google Scholar 

  157. F. Herrmann, I. Hinder, D. Shoemaker, P. Laguna and R. A. Matzner, Gravitational recoil from spinning binary black hole mergers. (2007) gr-qc/0701143.

    Google Scholar 

  158. I. Hinder, B. Vaishnav, F. Herrmann, D. Shoemaker and P. Laguna, Universality and final spin in eccentric binary black hole inspirals. (2007) arXiv:0710.5167 [gr-qc].

    Google Scholar 

  159. L. Hoffman and A. Loeb, Three-body kick to a bright quasar out of its galaxy during a merger. Astrophys. J. 638, L75 (2006)

    Article  ADS  Google Scholar 

  160. K. Holley-Bockelmann, K. Gultekin, D. Shoemaker and N. Yunes, Gravitational wave recoil and the retention of intermediate mass black holes. (2007) arXiv:0707.1334 [astro-ph].

    Google Scholar 

  161. S. A. Hughes, (Sort of) Testing relativity with extreme mass ratio inspirals. AIP Conf. Proc. 873 233 (2006).

    Article  ADS  Google Scholar 

  162. S. A. Hughes, LISA sources and science. (2007) arXiv:0711.0188 [gr-qc].

    Google Scholar 

  163. M. F. Huq, M. W. Choptuik and R. A. Matzner, Locating boosted Kerr and Schwarzschild apparent horizons. Phys. Rev. D 66, 084024 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  164. R. A. Hulse and J. H. Taylor, Discovery of a pulsar in a binary system. Astrophys. J. 195, L51 (2004).

    Article  ADS  Google Scholar 

  165. S. Husa, J. A. González, M. D. Hannam, B. Brügmann and U. Sperhake, Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing. (2007) arXiv:0706.0740 [gr-qc].

    Google Scholar 

  166. J. L. Jaramillo, E. Gourgoulhon and G. A. Mena Marugan, Inner boundary conditions for black hole Initial Data derived from Isolated Horizons. Phys. Rev. D 70, 124036 (2004).

    Article  ADS  Google Scholar 

  167. J. L. Jaramillo, J. A. Valiente Kroon and E. Gourgoulhon, From geometry to numerics: Interdisciplinary aspects in mathematical and numerical relativity. (2007) arXiv:0712.2332.

    Google Scholar 

  168. R. P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237 (1963).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  169. R. P. Kerr and A. Schild (1965), Some algebraically degenerate solutions of Einstein’s gravitational field equations. Proc. Symp. Appl. {M}ath. XVII, (pp. 199–209).

    MathSciNet  Google Scholar 

  170. L. E. Kidder, C. M. Will and A. G. Wiseman, Innermost stable orbits for coalescing binary systems of compact objects. Class. Quant. Grav. 9 L125 (1992).

    Article  ADS  Google Scholar 

  171. L. Kidder, Coalescing binary systems of compact objects to (post)$^5/2$-Newtonian order. V. Spin effects. Phys. Rev. D 52 821 (1995).

    Google Scholar 

  172. 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. D. 64, 064017 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  173. L. E. Kidder, L. Lindblom, M. A. Scheel, L. T. Buchman and H. P. Pfeiffer, Boundary conditions for the Einstein evolution system. Phys. Rev. D. 71, 064020 (2005).

    Article  ADS  Google Scholar 

  174. W. Kinnersley, Type D vacuum metrics. J. Math. Phys. 10, 1195 (1969).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  175. M. Koppitz et al., Recoil Velocities from Equal-Mass Binary-Black-Hole Mergers. Phys. Rev. Lett. 99, 041102 (2007).

    Article  ADS  Google Scholar 

  176. J. Kormendy and D. Richstone, Inward bound – The search for supermassive black holes in galactic nuclei. ARA&A 33, 581 (1995).

    ADS  Google Scholar 

  177. B. Krishnan, Fundamental properties and applications of quasi-local black hole horizons. (2007) arXiv:0712.1575 [gr-qc].

    Google Scholar 

  178. J. P. Leahy and P. Parma (1992). Multiple outbursts in radio galaxies. In J. Roland, H. Sol and G. Pelletier (Eds.), 7.IAP Meeting: Extragalactic radio sources - from beams to jets (pp. 307–308).

    Google Scholar 

  179. E. W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry. Phys. Rev. D 34 384 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  180. L. Lehner and O. M. Moreschi, Dealing with delicate issues in waveform calculations. Phys. Rev. D. 76 124040 (2007).

    Article  ADS  Google Scholar 

  181. N. I. Libeskind, S. Cole, C. S. Frenk and J. C. Helly, The effect of gravitational recoil on black holes forming in a hierarchical universe. MNRAS 368, 1381 (2006).

    Article  ADS  Google Scholar 

  182. A. Lichnerowicz, L’integration des équations de la gravitation relativiste et le problème des $n$ corps. J. Math. Pures et Appl. 23, 37 (1944).

    MATH  MathSciNet  Google Scholar 

  183. S. Liebling, Singularity threshold of the nonlinear sigma model using 3D adaptive mesh refinement. Phys. Rev. D 66, 041703(R) (2002).

    Article  ADS  Google Scholar 

  184. L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen and O. Rinne, A new generalized harmonic evolution system. Class. Quant. Grav. 23, S447 (2006).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  185. Z. Lippai, Z. Frei and Z. Haiman, Prompt shocks in the gas disk around a recoiling supermassive black hole binary. (2006) arXiv:0801.0739 [astro-ph].

    Google Scholar 

  186. A. Loeb, Observable signatures of a black hole ejected by gravitational radiation recoil in a galaxy merger. Class. Quant. Grav. 23, L71 (2006).

    Article  Google Scholar 

  187. C. O. Lousto and Y. Zlochower, Further insight into gravitational recoil. (2007) arXiv:0708.4048.

    Google Scholar 

  188. H. Lück et al., Status of the GEO600 detector. Class. Quant. Grav. 23, L71 (2006).

    Article  ADS  Google Scholar 

  189. P. MacNeice et al., {PARAMESH: A parallel adaptive mesh refinement community toolkit}. Comput. Phys. Comm. 136, 330 (2000).

    Article  ADS  Google Scholar 

  190. P. Madau and E. Quataert, The effect of gravitational-wave recoil on the demography of massive black holes. Astrophys. J. 606, L17 (2004).

    Article  ADS  Google Scholar 

  191. P. Madau, M. J. Rees, M. Volonteri, F. Haardt and S. P. Oh, Early reionization by miniquasars. Astrophys. J. 604, 484 (2004).

    Article  ADS  Google Scholar 

  192. P. Magain et al., Discovery of a bright quasar without a massive host galaxy. Nature. 437, 381 (2005).

    Article  ADS  Google Scholar 

  193. P. Marronetti and R. A. Matzner, Solving the initial value problem of two black holes. Phys. Rev. Lett. 85, 5500 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  194. P. Marronetti, M. F. Huq, P. Laguna, L. Lehner, R. A. Matzner and D. Shoemaker, Approximate analytical solutions to the initial data problem of black hole binary systems. Phys. Rev. D 62, 024017 (2000).

    Article  ADS  Google Scholar 

  195. P. Marronetti, M. D. Duez, S. L. Shapiro and T. Baumgarte, Dynamical determination of the innermost stable circular orbit of binary neutron stars. Phys. Rev. Lett. 92, 141101 (2004).

    Article  ADS  Google Scholar 

  196. R. A. Matzner, M. F. Huq and D. Shoemaker, Initial data and coordinates for multiple black hole systems. Phys. Rev. D 59, 024015 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  197. D. Merritt and L. Ferrarese, Black hole demographics from the M•-σ relation. MNRAS 320, L30 (2001).

    Article  ADS  Google Scholar 

  198. D. Merritt and R. D. Ekers, Tracing black hole mergers through radio lobe morphology. Science 297, 1310 (2002).

    Article  ADS  Google Scholar 

  199. D. Merritt, M. Milosavljević, M. Favata, S. Hughes and D. Holz, Consequences of gravitational radiation recoil. Astrophys. J. 607, L7 (2004).

    Article  ADS  Google Scholar 

  200. D. Merritt et al., The nature of the HE0450-2958 system. MNRAS 367, 1746 (2006).

    Article  ADS  Google Scholar 

  201. M. Miller, P. Gressman and W.-M. Suen,, Towards a realistic neutron star binary inspiral: Initial data and multiple orbit evolution in full general relativity. Phys. Rev. D. 69, 064026 (2004).

    Article  ADS  Google Scholar 

  202. M. Milosavljević and D. Merrit, Formation of galactic nuclei. Astrophys. J. 563, 34 (2001).

    Article  ADS  Google Scholar 

  203. C. W. Misner and J. A. Wheeler, Classical physics as geometry. Ann. Phys. (N.Y.). 2, 525 (1957).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  204. C. W. Misner, Wormhole initial conditions. Phys. Rev. 118, 1110 (1960).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  205. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation. (W. H. Freeman, New York, 1973).

    Google Scholar 

  206. V. Moncrief, Gravitational perturbations of spherically symmetric systems. I. The exterior problem. Ann. Phys. 88, 323 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  207. G. Nagy, O. E. Ortiz and O. A. Reula, Strongly hyperbolic second order Einstein’s evolution equations. Phys. Rev. D. 70, 044012 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  208. A. Nerozzi, C. Beetle, M. Bruni, L. M. Burko and D. Pollney, Towards wave extraction in numerical relativity: The quasi-Kinnersley frame. Phys. Rev. D. 72 024014 (2005).

    Article  ADS  Google Scholar 

  209. A. Nerozzi, M. Bruni, V. Re and L. M. Burko, Towards a wave-extraction method for numerical relativity: IV. Testing the quasi-Kinnersley method in the Bondi-Sachs framework. Phys. Rev. D. 73 044020 (2006).

    Article  ADS  Google Scholar 

  210. A. Nerozzi, Scalar functions for wave extraction in numerical relativity. Phys. Rev. D. 75 104002 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  211. E. T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. 3 566 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  212. R. O’Leary, E. O’Shaughnessy and F. Rasio, Dynamical interactions and the black hole merger rate of the universe. Phys. Rev. D. 76, 061504 (2007).

    Article  ADS  Google Scholar 

  213. N. ó Murchadha and J. W. York Jr., Initial-value problem of general relativity. I. General formulation and interpretation. Phys. Rev. D. 10, 428 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  214. N. Ó Murchadha and J. W. York Jr., Initial-value problem of general relativity. II. Stability of solution of the initial-value equations. Phys. Rev. D. 10, 437 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  215. N. Ó Murchadha and J. W. York Jr., Gravitational potentials: A constructive approach to genera l relativity. Gen. Relativ. Gravit. 7, 257 (1976).

    Article  ADS  Google Scholar 

  216. openGR homepage. url: http://wwwrel.ph.utexas.edu/openGR/. Cited 29 Jan 2008.

  217. C. Palenzuela, L. Lehner and S. L. Liebling, Orbital dynamics of binary boson star systems. (2007) arXiv:0706.2435 [gr-qc].

    Google Scholar 

  218. Y. Pan et al., A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: Nonspinning case. Phys. Rev. D 77, 012014 (2008).

    Article  Google Scholar 

  219. P. Parma, R. D. Ekers and R. Fanti, High resolution radio observations of low luminosity radio galaxies. Astron. Astrophys. Suppl. Ser. 59 511 (1985).

    ADS  Google Scholar 

  220. A. Peres, Classical radiation recoil. Phys. Rev. 128, 2471 (1962).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  221. P. C. Peters, Gravitational {r}adiation and the motion of two point masses. Phys. Rev. 136, B1224 (1964).

    Article  ADS  Google Scholar 

  222. H. P. Pfeiffer, S. A. Teukolsky and G. B. Cook, Quasicircular orbits for spinning binary black holes. Phys. Rev. D 62 104018 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  223. H. Pfeiffer (2003). Initial data for black hole evolutions Phd Thesis, Cornell University, gr-qc/0510016.

    Google Scholar 

  224. H. P. Pfeiffer et al., Reducing orbital eccentricity in binary black hole simulations. (2005) gr-qc/0702106.

    Google Scholar 

  225. E. Poisson, The motion of point particles in curved spacetime. Living Rev. Relativity 2004-6 url: http://relativity.livingreviews.org/Articles/lrr-2004-6/download/index.html. Cited 29 Jan 2008.

  226. F. Pretorius, Numerical relativity using a generalized harmonic decomposition. Class. Quant. Grav. 22, 425 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  227. F. Pretorius, Evolution of binary black-hole spacetimes. Phys. Rev. Lett. 95, 121101 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  228. F. Pretorius and M. W. Choptuik, Adaptive mesh refinement for coupled elliptic-hyperbolic systems. J. Comput. Phys. 218, 246 (2006).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  229. F. Pretorius, Simulation of binary-black-hole spacetimes with a harmonic evolution scheme. Class. Quant. Grav. 23, 529 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  230. F. Pretorius and D. Khurana, Black hole mergers and unstable circular orbits. Class. Quant. Grav. 24, S83 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  231. F. Pretorius, Binary black hole coalescence. (2007) arXiv:0710.1338.

    Google Scholar 

  232. B. Reimann, Constraint and gauge shocks in one-dimensional numerical relativity. Phys. Rev. D. 71, 064021 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  233. L. Rezzolla et al., Spin diagrams for equal-mass black-hole binaries with aligned spins. (2007) arXiv:0708.3999.

    Google Scholar 

  234. L. Rezzolla et al., The final spin from the coalescence of aligned-spin black-hole binaries. (2007) arXiv:0710.3345 [gr-qc].

    Google Scholar 

  235. L. Rezzolla et al., On the final spin from the coalescence of two black holes. (2007) arXiv:0712.3541 [gr-qc].

    Google Scholar 

  236. R. K. Sachs, Gravitational waves in general relativity. Proc. Roy. Soc. A. 270, 103 (1962).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  237. Samrai homepage. url: https://computation.llnl.gov/casc/SAMRAI/. Cited 29 Jan 2008.

  238. O. Sarbach, G. Calabrese, J. Pullin and M. Tiglio, Hyperbolicity of the BSSN system of Einstein evolution equations. Phys. Rev. D. 66, 064022 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  239. O. Sarbach and M. Tiglio, Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein’s equations. Phys. Rev. D. 66, 064023 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  240. O. Sarbach and M. Tiglio, Boundary conditions for Einstein’s field equations: Analytical and numerical analysis. J. Hyperbol. Diff. Equat. 2, 839 (2004).

    Article  MathSciNet  Google Scholar 

  241. M. A. Scheel et al., Solving Einstein’s equations with dual coordinate frames. Phys. Rev. D 74, 104006 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  242. E. Schnetter, S. H. Hawley and I. Hawke, Evolutions in 3{D} numerical relativity using fixed mesh refinement. Class. Quant. Grav. 21, 1465 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  243. J. D. Schnittman and A. Buonanno, The distribution of recoil velocities from merging black holes. (2007) astro-ph/0702641.

    Google Scholar 

  244. J. D. Schnittman et al., Anatomy of the binary black hole recoil: {A} multipolar analysis. (2007) arXiv:0707.0301 [astro-ph].

    Google Scholar 

  245. E. Seidel, Towards a singularity-proof scheme in numerical relativity. Phys. Rev. Lett. 69, 1845 (1992).

    Article  ADS  Google Scholar 

  246. M. Shibata and T. Nakamura, Evolution of three-dimensional gravitational waves: Harmonic slicing case. Phys. Rev. D. 52, 5428 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  247. M. Shibata, K. Taniguchi and K. Uryu, Merger of binary neutron stars of unequal mass in full general relativity. Phys. Rev. D. 68, 084020 (2003).

    Article  ADS  Google Scholar 

  248. M. Shibata and K. Taniguchi, Merger of black hole and neutron star in general relativity: {T}idal disruption, torus mass, and gravitational waves. (2003) arXiv:0711.1410 [astro-ph].

    Google Scholar 

  249. D. Shoemaker, K. Smith, U. Sperhake, P. Laguna, E. Schnetter and D. Fiske, Moving black holes via singularity excision. Class. Quant. Grav. 20, 3729 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  250. L. Smarr (1975). The structure of general relativity with a numerical illustration: The collision of two black holes Phd Thesis, University of Texas at Austin.

    Google Scholar 

  251. L. Smarr, A. Čadež, B. DeWitt and K. Eppley, Collision of two black holes: Theoretical framework. Phys. Rev. D 14, 2443 (1976).

    Article  ADS  Google Scholar 

  252. L. Smarr., Space-times generated by computers: {Black} holes with gravitational radiation. Ann. N. Y. Acad. Sciences. 302, 569 (1977).

    Article  ADS  Google Scholar 

  253. L. Smarr and J. W. York Jr., Kinematical conditions in the construction of spacetime. Phys. Rev. D. 17, 2529 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  254. C. F. Sopuerta, N. Yunes and P. Laguna, Gravitational recoil from binary black hole mergers: The close limit approximation. Phys. Rev. D 74 124010 (2006).

    Google Scholar 

  255. C. F. Sopuerta, N. Yunes and P. Laguna, Gravitational recoil velocities from eccentric binary black hole mergers. Astrophys. J. 656 L9 (2007).

    Article  ADS  Google Scholar 

  256. U. Sperhake, B. Kelly, P. Laguna, K. L. Smith and E. Schnetter, Black-hole head-on collisions and gravitational waves with fixed mesh-refinement and dynamic singularity excision. Phys. Rev. D. 71, 124042 (2005).

    Article  ADS  Google Scholar 

  257. U. Sperhake, Binary black-hole evolutions of excision and puncture data. Phys. Rev. D. 76, 104015 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  258. U. Sperhake, E. Berti, V. Cardoso, J. A. González and B. Brügmann, Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity. (2007) arXiv:0710.3823 [gr-qc].

    Google Scholar 

  259. D. Tatsumi et al., Current status of Japanese detectors. (2007) arXiv:0704.2881 [gr-qc].

    Google Scholar 

  260. J. H. Taylor and J. M. Weisberg, Further experimental tests of relativistic gravity using the binary pulsar PSR 1913+16. Astrophys. J. 345, 434 (1989).

    Article  ADS  Google Scholar 

  261. J. Thornburg, Coordinates and boundary conditions for the general relativistic initial data problem. Class. Quant. Grav. 54, 1119 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  262. J. Thornburg, A Fast Apparent-Horizon Finder for 3-Dimensional {C}artesian Grids in numerical relativity. Class. Quant. Grav. 21, 743 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  263. K. S. Thorne, Multipole expansions of gravitational radiation. Rev. Mod. Phys. 52 299 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  264. W. Tichy, B. Brügmann and P. Laguna, Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector. Phys. Rev. D 68, 064008 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  265. W. Tichy and B. Brügmann, Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions. Phys. Rev. D 69, 024006 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  266. B. Vaishnav, I. Hinder, F. Herrmann and D. Shoemaker, Matched filtering of numerical relativity templates of spinning binary black holes. (2007) arXiv:0705.3829 [gr-qc].

    Google Scholar 

  267. J. R. van Meter, J. G. Baker, M. Koppitz and D.-I. Choi, How to move a black hole without excision: Gauge conditions for the numerical evolution of a moving puncture. Phys. Rev. D. 73, 124011 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  268. M. Volonteri, F. Haardt and P. Madau, The assembly and merging history of supermassive black holes in hierarchical models of galaxy formation. Astrophys. J. 582, 559 (2003).

    Article  ADS  Google Scholar 

  269. M. Volonteri and R. Perna, Dynamical evolutions of intermediate-mass black holes and their observational signatures in the nearby universe. MNRAS 358, 913 (2005).

    Article  ADS  Google Scholar 

  270. M. Volonteri, G. Lodato and P. Natarajan, The evolution of massive black hole seeds. (2007) arXiv:0709.0529 [astro-ph].

    Google Scholar 

  271. M. Volonteri, F. Haardt and K. Gultekin, Compact massive objects in Virgo galaxies: The black hole population. (2007) arXiv:0710.5770 [astro-ph].

    Google Scholar 

  272. J. Winicour, Characteristic evolution and matching. Living Rev. Relativity 2005-10 url: http://relativity.livingreviews.org/Articles/lrr-2005-10/download/index.html. Cited 29 Jan 2008}.

  273. H.-J. Yo, T. W. Baumgarte and S. L. Shapiro, Improved numerical stability of stationary black hole evolution calculations. Phys. Rev. D 66, 084026 (2002).

    Article  MathSciNet  Google Scholar 

  274. J. W. York Jr., Gravitational degrees of freedom and the initial-value problem. Phys. Rev. Lett. 26, 1656 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  275. J. W. York Jr., Role of conformal three-geometry in the dynamics of gravitation. Phys. Rev. Lett. 28, 1082 (1972).

    Article  ADS  Google Scholar 

  276. J. W. York Jr., Covariant decompositions of symmetric tensors in the theory of gravitation. Ann. Inst. Henri Poincaré A. 21, 319 (1974).

    ADS  MathSciNet  Google Scholar 

  277. J. W. York Jr., Kinematics and dynamics of general relativity. In L. Smarr (Ed.), Sources of Gravitational Radiation (Cambirdge University Press, Cambridge, 1979), (pp. 82–126).

    Google Scholar 

  278. J. W. York Jr. and T. Piran, The initial value problem and beyond. In R. A. Matzner and L. C. Shepley (Eds.), Spacetime and Geometry (1982), (pp. 147–176).

    Google Scholar 

  279. J. W. York Jr., The initial value problem and dynamics. In N. Derielle & T. Piran (Eds.), Gravitational Radiation (North-Holland Publishing Company, 1979) (pp. 175–201).

    Google Scholar 

  280. J. W. York Jr., Conformal ‘thin-sandwich’ data for the initial-value problem of general relativity. Phys. Rev. Lett. 82, 1350 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  281. F. J. Zerilli, Tensor harmonics in canonical form for gravitational radiation and other applications. Phys. Rev. Lett. 82, 1350 (1999).

    Article  MathSciNet  Google Scholar 

  282. Y. Zlochower, J. G. Baker, M. Campanelli and C. O. Lousto, Accurate black hole evolutions by fourth-order numerical relativity. Phys. Rev. D 72, 024021 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sperhake, U. (2009). Colliding Black Holes and Gravitational Waves. In: Papantonopoulos, E. (eds) Physics of Black Holes. Lecture Notes in Physics, vol 769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88460-6_4

Download citation

Publish with us

Policies and ethics