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Numerical relativity: the role of black holes in gravitational wave physics, astrophysics and high-energy physics

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Abstract

Black holes play an important role in many areas of physics. Their modeling in the highly-dynamic, strong-field regime of general relativity requires the use of computational methods. We present a review of the main results obtained through numerical relativity simulations of black-hole spacetimes with a particular focus on the most recent developments in the areas of gravitational-wave physics, astrophysics, high-energy collisions, the gauge-gravity duality, and the study of fundamental properties of black holes.

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Notes

  1. Strictly speaking, this depends on the choice of gauge conditions.

References

  1. Aasi, J., et al.: The NINJA-2 project: Detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations. Class. Quantum Grav. LIGO-P1300199 (2014). ArXiv:1401.0939 [gr-qc]

  2. Aharony, O., Gubser, S.S., Maldacena, J.M., Ooguri, H., Oz, Y.: Large N field theories, string theory and gravity. Phys. Rep. 323, 183–386 (2000). doi:10.1016/S0370-1573(99)00083-6. Hep-th/9905111

    ADS  MathSciNet  Google Scholar 

  3. Ajith, P.: Gravitational-wave data analysis using binary black-hole waveforms. Class. Quantum Grav. 25, 114033 (2008). ArXiv:0712.0343 [gr-qc]

    ADS  Google Scholar 

  4. Ajith, P., Hannam, M., Husa, S., Chen, Y., Brügmann, B., et al.: Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins. Phys. Rev. Lett. 106, 241101 (2011). doi:10.1103/PhysRevLett.106.241101. ArXiv:0909.2867 [gr-qc]

    ADS  Google Scholar 

  5. Ajith, P., et al.: Phenomenological template family for black-hole coalescence waveforms. Class. Quantum Grav. 24, S689–S700 (2007). doi:10.1088/0264-9381/24/19/S31. ArXiv:0704.3764 [gr-qc]

    ADS  MATH  MathSciNet  Google Scholar 

  6. Ajith, P., et al.: A template bank for gravitational waveforms from coalescing binary black holes: I. Non-spinning binaries. Phys. Rev. D 77, 104017 (2008). ArXiv:0710.2335 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  7. Ajith, P., et al.: The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries. Class. Quantum Grav. 29, 124001 (2012). doi:10.1088/0264-9381/29/12/124001. ArXiv:1201.5319 [gr-qc]

    ADS  Google Scholar 

  8. Alcubierre, M.: Introduction to 3+1 Numerical Relativity. Oxford University Press, Oxford (2008)

    MATH  Google Scholar 

  9. Alic, D., Bona-Casas, C., Bona, C., Rezzolla, L., Palenzuela, C.: Conformal and covariant formulation of the Z4 system with constraint-violation damping. Phys. Rev. D 85, 064040 (2012). doi:10.1103/PhysRevD.85.064040. ArXiv:1106.2254 [gr-qc]

    ADS  Google Scholar 

  10. Alic, D., Mösta, P., Rezzolla, L., Zanotti, O., Jaramillo, J.L.: Accurate simulations of binary black-hole mergers in force-free electrodynamics. Astrophys. J. 754, 36 (2012). doi:10.1088/0004-637X/754/1/36. ArXiv:1204.2226 [gr-qc]

    ADS  Google Scholar 

  11. Anderson, M., Lehner, L., Megevand, M., Neilsen, D.: Post-merger electromagnetic emissions from disks perturbed by binary black holes. Phys. Rev. D 81, 044004 (2010). doi:10.1103/PhysRevD.81.044004. ArXiv:0910.4969 [astro-ph]

    ADS  Google Scholar 

  12. Ansorg, M., Brügmann, B., Tichy, W.: A single-domain spectral method for black hole puncture data. Phys. Rev. D 70, 064011 (2004). doi:10.1103/PhysRevD.70.064011. Gr-qc/0404056

    ADS  Google Scholar 

  13. Antoniadis, I.: A Possible new dimension at a few TeV. Phys. Lett. B 246, 377–384 (1990). doi:10.1016/0370-2693(90)90617-F

    ADS  MathSciNet  Google Scholar 

  14. Antoniadis, I., Arkani-Hamed, N., Dimopoulos, S., Dvali, G.R.: New dimensions at a millimeter to a Fermi and superstrings at a TeV. Phys. Lett. B 436, 257–263 (1998). doi:10.1016/S0370-2693(98)00860-0. Hep-ph/9804398

    ADS  Google Scholar 

  15. Arkani-Hamed, N., Dimopoulos, S., Dvali, G.R.: The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B 429, 263–272 (1998). doi:10.1016/S0370-2693(98)00466-3. Hep-ph/9803315

    ADS  Google Scholar 

  16. Aylott, B., et al.: Status of NINJA: the Numerical INJection Analysis project. Class. Quantum Grav. 26, 114008 (2009). doi:10.1088/0264-9381/26/11/114008. ArXiv:0905.4227 [gr-qc]

    ADS  Google Scholar 

  17. Aylott, B., et al.: Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project. Class. Quantum Grav. 26, 165008 (2009). doi:10.1088/0264-9381/26/16/165008. ArXiv:0901.4399 [gr-qc]

    ADS  Google Scholar 

  18. Baker, J.G., Centrella, J., Choi, D.I., Koppitz, M., van Meter, J.: Gravitational-wave extraction from an inspiraling configuration of merging black holes. Phys. Rev. Lett. 96, 111102 (2006). doi:10.1103/PhysRevLett.96.111102. Gr-qc/0511103

    ADS  Google Scholar 

  19. Balasubramanian, V., Kraus, P.: A stress tensor for anti-de Sitter gravity. Commun. Math. Phys. 208, 413–428 (1999). doi:10.1007/s002200050764. Hep-th/9902121

    ADS  MATH  MathSciNet  Google Scholar 

  20. Banks, T., Fischler, W.: A model for high energy scattering in quantum gravity (1999). Report number RU-99–23, UTTP-03-99. Hep-th/9906038

  21. Bantilan, H., Pretorius, F., Gubser, S.S.: Simulation of asymptotically AdS5 spacetimes with a generalized harmonic evolution scheme. Phys. Rev. D 85, 084038 (2012). doi:10.1103/PhysRevD.85.084038. ArXiv:1201.2132 [hep-th]

    ADS  Google Scholar 

  22. Baumgarte, T.W., Shapiro, S.L.: On the numerical integration of Einstein’s field equations. Phys. Rev. D 59, 024007 (1998). doi:10.1103/PhysRevD.59.024007. Gr-qc/9810065

    ADS  MathSciNet  Google Scholar 

  23. Baumgarte, T.W., Shapiro, S.L.: Numerical Relativity. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  24. Bayona, C.A., Braga, N.R.: Anti-de Sitter boundary in Poincare coordinates. Gen. Relativ. Gravit. 39, 1367–1379 (2007). doi:10.1007/s10714-007-0446-y. Hep-th/0512182

    ADS  MATH  Google Scholar 

  25. Bekenstein, J.D.: Extraction of energy and charge from a black hole. Phys. Rev. D 7, 949–953 (1973). doi:10.1103/PhysRevD.7.949

    ADS  MathSciNet  Google Scholar 

  26. Bekenstein, J.D.: Gravitational-radiation recoil and runaway black holes. Astrophys. J. 183, 657–664 (1973). doi:10.1086/152255

    ADS  Google Scholar 

  27. Berti, E., Cardoso, V., Gualtieri, L., Horbatsch, M., Sperhake, U.: Numerical simulations of single and binary black holes in scalar-tensor theories: circumventing the no-hair theorem. Phys. Rev. D 87, 124020 (2013). doi:10.1103/PhysRevD.87.124020. ArXiv:1304.2836 [gr-qc]

    ADS  Google Scholar 

  28. Berti, E., Kesden, M., Sperhake, U.: Effects of post-Newtonian spin alignment on the distribution of black-hole recoils. Phys. Rev. D 85, 124049 (2012). doi:10.1103/PhysRevD.85.124049. ArXiv:1203.2920 [astro-ph]

    ADS  Google Scholar 

  29. Bizoń, P., Rostworowski, A.: On weakly turbulent instability of anti-de Sitter space. Phys. Rev. Lett. 107, 031102 (2011). doi:10.1103/PhysRevLett.107.031102. ArXiv:1104.3702 [gr-qc]

    ADS  Google Scholar 

  30. Blanchet, L.: Gravitational radiation from post-Newtonian sources and inspiralling compact binaries. Living Rev. Rel. 9(4) (2006). http://www.livingreviews.org/lrr-2006-4

  31. Blandford, R.D., Znajek, R.L.: Electromagnetic extractions of energy from Kerr black holes. Mon. Not. Roy. Astron. Soc. 179, 433–456 (1977)

    ADS  Google Scholar 

  32. Bode, T., Haas, R., Bogdanović, T., Laguna, P., Shoemaker, D.: Relativistic mergers of supermassive black holes and their electromagnetic signatures. Astrophys. J. 715, 1117–1131 (2010). doi:10.1088/0004-637X/715/2/1117. ArXiv:0912.0087 [gr-qc]

    ADS  Google Scholar 

  33. Bode, T., et al.: Mergers of supermassive black holes in astrophysical environments. Astrophys. J. 744, 45 (2011). doi:10.1088/0004-637X/744/1/45. ArXiv:1101.4684 [gr-qc]

    ADS  Google Scholar 

  34. Bogdanović, T., Reynolds, C.S., Miller, M.C.: Alignment of the spins of supermassive black holes prior to coalescence. Astrophys. J. 661, L147–L150 (2007). Astro-ph/0703054

    ADS  Google Scholar 

  35. Bona, C., Ledvinka, T., Palenzuela, C., Žáček, M.: General-covariant evolution formalism for numerical relativity. Phys. Rev. D 67, 104005 (2003). doi:10.1103/PhysRevD.67.104005. Gr-qc/0302083

    ADS  MathSciNet  Google Scholar 

  36. Bona, C., Palenzuela-Luque, C., Bona-Casas, C.: Elements of Numerical Relativity and Relativistic Hydrodynamics. Springer, London, New York (2009)

    MATH  Google Scholar 

  37. Bonnor, W.B., Rotenberg, M.A.: Transport of momentum by gravitational waves: the linear approximation. Proc. R. Soc. Lond. A. 265, 109–116 (1961)

    ADS  MathSciNet  Google Scholar 

  38. Brown, D.A., Lundgren, A., O’Shaughnessy, R.: Nonspinning searches for spinning binaries in ground-based detector data: amplitude and mismatch predictions in the constant precession cone approximation. Phys. Rev. D 86, 064020 (2012). doi:10.1103/PhysRevD.86.064020. ArXiv:1203.6060 [gr-qc]

    ADS  Google Scholar 

  39. Brown, J.D., York Jr, J.W.: Quasilocal energy and conserved charges derived from the gravitational action. Phys. Rev. D 47, 1407–1419 (1993). doi:10.1103/PhysRevD.47.1407. Gr-qc/9209012

    ADS  MathSciNet  Google Scholar 

  40. Buchel, A., Lehner, L., Liebling, S.L.: Scalar collapse in AdS. Phys. Rev. D 86, 123011 (2012). doi:10.1103/PhysRevD.86.123011. ArXiv:1210.0890 [gr-qc]

    ADS  Google Scholar 

  41. Buchel, A., Liebling, S.L., Lehner, L.: Boson stars in AdS. Phys. Rev. D 87, 123006 (2013). doi:10.1103/PhysRevD.87.123006. ArXiv:1304.4166 [gr-qc]

    ADS  Google Scholar 

  42. Buonanno, A., Chen, Y., Valisneri, M.: Detection template families for gravitational waves from the final stages of binary-black-hole inspirals: Nonspinning case. Phys. Rev. D 67, 024016 (2003). [Erratum-ibid. 74, 029903 (2006)] gr-qc/0205122.

  43. Buonanno, A., Damour, T.: Effective one-body aproach to general relativistic two-body dynamics. Phys. Rev. D 59, 084006 (1999)

    ADS  MathSciNet  Google Scholar 

  44. Buonanno, A., Damour, T.: Transition from inspiral to plunge in binary black hole coalescences. Phys. Rev. D 62, 064015 (2000)

    ADS  Google Scholar 

  45. Campanelli, M., Lousto, C.O., Marronetti, P., Zlochower, Y.: Accurate evolutions of orbiting black-hole binaries without excision. Phys. Rev. Lett. 96, 111101 (2006). doi:10.1103/PhysRevLett.96.111101. Gr-qc/0511048

    ADS  Google Scholar 

  46. Campanelli, M., Lousto, C.O., Zlochower, Y.: Spinning-black-hole binaries: the orbital hang up. Phys. Rev. D 74, 041501 (2006). doi:10.1103/PhysRevD.74.041501. Gr-qc/0604012

    ADS  MathSciNet  Google Scholar 

  47. Campanelli, M., Lousto, C.O., Zlochower, Y., Merritt, D.: Large merger recoils and spin flips from generic black-hole binaries. Astrophys. J. 659, L5–L8 (2007). doi:10.1086/516712. Gr-qc/0701164

    ADS  Google Scholar 

  48. Campanelli, M., Lousto, C.O., Zlochower, Y., Merritt, D.: Maximum gravitational recoil. Phys. Rev. Lett. 98, 231102 (2007). Gr-qc/0702133

    ADS  Google Scholar 

  49. Cao, Z., Hilditch, D.: Numerical stability of the Z4c formulation of general relativity. Phys. Rev. D 85, 124032 (2012). doi:10.1103/PhysRevD.85.124032. ArXiv:1111.2177 [gr-qc]

    ADS  Google Scholar 

  50. Centrella, J.M., Baker, J.G., Kelly, B.J., van Meter, J.R.: Black-hole binaries, gravitational waves, and numerical relativity. Rev. Mod. Phys. 82, 3069 (2010). doi:10.1103/RevModPhys.82.3069. ArXiv:1010.5260 [gr-qc]

    Google Scholar 

  51. Chang, P., Strubbe, L.E., Menou, K., Quataert, E.: Fossil gas and the electromagnetic precursor of supermassive binary black hole mergers. MNRAS 407, 2007–2016 (2010). ArXiv:0906.0825 [astro-ph]

    ADS  Google Scholar 

  52. Chesler, P.M., Yaffe, L.G.: Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma. Phys. Rev. Lett. 102, 211601 (2009). doi:10.1103/PhysRevLett.102.211601. ArXiv:0812.2053 [hep-th]

    ADS  MathSciNet  Google Scholar 

  53. Chesler, P.M., Yaffe, L.G.: Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory. Phys. Rev. D 82, 026006 (2010). doi:10.1103/PhysRevD.82.026006. ArXiv:0906.4426 [hep-th]

    ADS  Google Scholar 

  54. Chesler, P.M., Yaffe, L.G.: Holography and colliding gravitational shock waves in asymptotically \(AdS_5\) spacetime. Phys. Rev. Lett. 106, 021601 (2011). doi: 10.1103/PhysRevLett.106.021601. ArXiv:1011.3562 [hep-th]

    ADS  Google Scholar 

  55. Chesler, P.M., Yaffe, L.G.: Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes (2013). ArXiv:1309.1439 [hep-th]

  56. Choptuik, M.W.: Universality and scaling in graviational collapse of a massless scalar field. Phys. Rev. Lett. 70, 9–12 (1993). doi:10.1103/PhysRevLett.70.9

    ADS  Google Scholar 

  57. Choptuik, M.W., Pretorius, F.: Ultra relativistic particle collisions. Phys. Rev. Lett. 104, 111101 (2010). doi:10.1103/PhysRevLett.104.111101. ArXiv:0908.1780 [gr-qc]

    ADS  Google Scholar 

  58. Dai, D.C., Starkman, G., Stojkovic, D., Issever, C., Rizvi, E., et al.: BlackMax: a black-hole event generator with rotation, recoil, split branes, and brane tension. Phys. Rev. D 77, 076007 (2008). doi:10.1103/PhysRevD.77.076007. ArXiv:0711.3012 [hep-ph]

    ADS  Google Scholar 

  59. Damour, T., Nagar, A.: Comparing effective-one-body gravitational waveforms to accurate numerical data. Phys. Rev. D 77, 024043 (2008). ArXiv:0711.2628 [gr-qc]

    ADS  Google Scholar 

  60. Damour, T., Nagar, A., Hannam, M.D., Husa, S., Brügmann, B.: Accurate effective-one-body waveforms of inspiralling and coalescing black-hole binaries. Phys. Rev. D 78, 044039 (2008). ArXiv:[0803.3162]

    ADS  Google Scholar 

  61. Damour, T., Trias, M., Nagar, A.: Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries. Phys. Rev. D 83, 024006 (2011). doi:10.1103/PhysRevD.83.024006. ArXiv:1009.5998 [gr-qc]

    ADS  Google Scholar 

  62. Dias, O.J.C., Horowitz, G.T., Marolf, D., Santos, J.E.: On the nonlinear stability of asymptotically anti-de sitter solutions. Class. Quantum Grav. 29, 235019 (2012). doi:10.1088/0264-9381/29/23/235019. ArXiv:1208.5772 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  63. Dimopoulos, S., Landsberg, G.: Black Holes at the LHC. Phys. Rev. Lett. 87, 161602 (2001). doi:10.1103/PhysRevLett.87.161602. Hep-th/0106295

    ADS  Google Scholar 

  64. Dolan, S.R.: Superradiant instabilities of rotating black holes in the time domain. Phys. Rev. D 87, 124026 (2013). doi:10.1103/PhysRevD.87.124026. ArXiv:1212.1477 [gr-qc]

    ADS  Google Scholar 

  65. Drude, P.: Zur elektronentheorie der metalle. Annalen der Physik 306, 566 (1900). doi:10.1002/andp.19003060312

    ADS  Google Scholar 

  66. Drude, P.: Zur elektronentheorie der metalle: II. Teil. galvanomagnetische und thermomagnetische effekte. Annalen der Physik 308, 369 (1900). doi:10.1002/andp.19003081102

    ADS  Google Scholar 

  67. Eardley, D.M., Giddings, S.B.: Classical black hole production in high-energy collisions. Phys. Rev. D 66, 044011 (2002). doi:10.1103/PhysRevD.66.044011. Gr-qc/0201034

    ADS  MathSciNet  Google Scholar 

  68. East, W.E., Pretorius, F.: Ultrarelativistic black hole formation. Phys. Rev. Lett. 110, 101101 (2013). doi:10.1103/PhysRevLett.110.101101. ArXiv:1210.0443 [gr-qc]

    ADS  Google Scholar 

  69. Emparan, R., Reall, H.S.: Black holes in higher dimensions. Living Rev. Rel. 11(6) (2008). http://www.livingreviews.org/lrr-2008-6

  70. Farris, B.D., Gold, R., Paschalidis, V., Etienne, Z.B., Shapiro, S.L.: Binary black hole mergers in magnetized disks: simulations in full general relativity. Phys. Rev. Lett. 109, 221102 (2012). doi:10.1103/PhysRevLett.109.221102. ArXiv:1207.3354 [astro-ph]

    ADS  Google Scholar 

  71. Farris, B.D., Liu, Y.T., Shapiro, S.L.: Binary black hole mergers in gaseous environments: ’Binary Bondi’ and ’Binary Bondi-Hoyle-Lyttleton’ accretion. Phys. Rev. D 81, 084008 (2010). doi:10.1103/PhysRevD.81.084008. ArXiv:0912.2096 [asttro-ph]

    ADS  Google Scholar 

  72. Finn, L.S.: Detection, measurement and gravitational radiation. Phys. Rev. D 46, 5236–5249 (1992). Gr-qc/9209010

    ADS  Google Scholar 

  73. Fitchett, M.J.: The influence of gravitational wave momentum losses on the centre of mass motion of a newtonian binary system. MNRAS 203, 1049–1062 (1983)

    ADS  MATH  Google Scholar 

  74. Frost, J.A., Gaunt, J.R., Sampaio, M.O.P., Casals, M., Dolan, S.R., et al.: Phenomenology of Production and Decay of Spinning Extra- Dimensional Black Holes at Hadron Colliders. JHEP 10, 014 (2009). doi:10.1088/1126-6708/2009/10/014. ArXiv:0904.0979 [hep-th]

    ADS  Google Scholar 

  75. Garfinkle, D.: Harmonic coordinate method for simulating generic singularities. Phys. Rev. D 65, 044029 (2002). doi:10.1103/PhysRevD.65.044029. Gr-qc/0110013

    ADS  MathSciNet  Google Scholar 

  76. Giddings, S.B., Thomas, S.: High energy colliders as black hole factories: the end of short distance physics. Phys. Rev. D 65, 056010 (2002). doi:10.1103/PhysRevD.65.056010. Hep-ph/0106219

    ADS  Google Scholar 

  77. González, J.A., Hannam, M.D., Sperhake, U., Brügmann, B., Husa, S.: Supermassive kicks for spinning black holes. Phys. Rev. Lett. 98, 231101 (2007). doi:10.1103/PhysRevLett.98.231101. Gr-qc/0702052

    ADS  Google Scholar 

  78. González, J.A., Sperhake, U., Brügmann, B., Hannam, M.D., Husa, S.: The maximum kick from nonspinning black-hole binary inspiral. Phys. Rev. Lett. 98, 091101 (2007). doi:10.1103/PhysRevLett.98.091101. Gr-qc/0610154

    ADS  MathSciNet  Google Scholar 

  79. Gregory, R., Laflamme, R.: Black strings and p-branes are unstable. Phys. Rev. Lett. 70, 2837–2840 (1993). doi:10.1103/PhysRevLett.70.2837. Hep-th/9301052

    ADS  MATH  MathSciNet  Google Scholar 

  80. Gregory, R., Laflamme, R.: The Instability of charged black strings and p-branes. Nucl. Phys. B 428, 399–434 (1994). doi:10.1016/0550-3213(94)90206-2. Hep-th/9404071

    ADS  MATH  MathSciNet  Google Scholar 

  81. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from non-critical string theory. Phys. Lett. B 428, 105–114 (1998). doi:10.1016/S0370-2693(98)00377-3. Hep-th/9802109

    ADS  MathSciNet  Google Scholar 

  82. Guedes, J., Madau, P., Mayer, L., Callegari, S.: Recoiling massive black holes in gas-rich galaxy mergers. Astrophys. J. 729, 125 (2011). ArXiv:1008.2032 [astro-ph]

    ADS  Google Scholar 

  83. Gundlach, C., Calabrese, G., Hinder, I., Martín-García, J.M.: Constraint damping in the Z4 formulation and harmonic gauge. Class. Quantum Grav. 22, 3767–3773 (2005). doi:10.1088/0264-9381/22/17/025

    MATH  Google Scholar 

  84. Haiman, Z., Loeb, A.: What is the highest plausible redshift of luminous quasars? Astrophys. J. 552, 459–463 (2001)

    ADS  Google Scholar 

  85. Hannam, M., et al.: Twist and shout: a simple model of complete precessing black-hole-binary gravitational waveforms (2013). ArXiv:1308.3271 [gr-qc]

  86. de Haro, S., Solodukhin, S.N., Skenderis, K.: Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence. Commun. Math. Phys. 217, 595–622 (2001). doi:10.1007/s002200100381. Hep-th/0002230

    ADS  MATH  Google Scholar 

  87. Harris, C.M., Richardson, P., Webber, B.R.: CHARYBDIS: a black hole event generator. JHEP 0308, 033 (2003). Hep-ph/0307305

    ADS  Google Scholar 

  88. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    MATH  Google Scholar 

  89. Healy, J., Bode, T., Haas, R., Pazos, E., Laguna, P., Shoemaker, D.M., Yunes, N.: Late inspiral and merger of binary black holes in scalar-tensor theories of gravity (2011). ArXiv:1112.3928 [gr-qc]

  90. Heller, M.P., Janik, R.A., Witaszczyk, P.: A numerical relativity approach to the initial value problem in asymptotically anti-de Sitter spacetime for plasma thermalization—an ADM formulation. Phys. Rev. D 85, 126002 (2012). doi:10.1103/PhysRevD.85.126002. ArXiv:1203.0755 [hep-th]

    ADS  Google Scholar 

  91. Heller, M.P., Janik, R.A., Witaszczyk, P.: The characteristics of thermalization of boost-invariant plasma from holography. Phys. Rev. Lett. 108, 201602 (2012). doi:10.1103/PhysRevLett.108.201602. ArXiv:1103.3452 [hep-th]

    ADS  Google Scholar 

  92. Heller, M.P., Mateos, D., van der Schee, W., Trancanelli, D.: Strong coupling isotropization of non-abelian plasmas simplified. Phys. Rev. Lett. 108, 191601 (2012). doi:10.1103/PhysRevLett.108.191601. ArXiv:1202.0981 [hep-th]

    ADS  Google Scholar 

  93. Hemberger, D.A., Lovelace, G., Loredo, T.J., Kidder, L.E., Scheel, M.A., Szilágyi, B., Taylor, N.W., Teukolsky, S.A.: Final spin and radiated energy in numerical simulations of binary black holes with equal masses and equal, aligned or anti-aligned spins. Phys. Rev. D 88, 064014 (2013). doi:10.1103/PhysRevD.88.064014. ArXiv:1305.5991 [gr-qc]

    ADS  Google Scholar 

  94. Hilditch, D., Bernuzzi, S., Thierfelder, M., Cao, Z., Tichy, W., Brügmann, B.: Compact binary evolutions with the Z4c formulation. Phys. Rev. D 88, 084057 (2013). doi:10.1103/PhysRevD.88.084057. ArXiv:1212.2901 [gr-qc]

    ADS  Google Scholar 

  95. Hinder, I., et al.: Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR collaboration . Class. Quant. Grav. 31, 025012 (2014). ArXiv:1307.5307 [gr-qc]

    Google Scholar 

  96. Horbatsch, M.W., Burgess, C.P.: Cosmic black-hole hair growth and quasar OJ287. J. Cosmol. Astropart. Phys. 1205, 010 (2012). doi:10.1088/1475-7516/2012/05/010. ArXiv:1111.4009 [gr-qc]

    ADS  Google Scholar 

  97. Horowitz, G.T., Hubeny, V.E.: Quasinormal modes of AdS black holes and the approach to thermal equilibrium. Phys. Rev. D 62, 024027 (2000). doi:10.1103/PhysRevD.62.024027. Hep-th/9909056

    ADS  MathSciNet  Google Scholar 

  98. Horowitz, G.T., Santos, J.E., Tong, D.: Further evidence for lattice-induced scaling. JHEP 1211, 102 (2012). doi:10.1007/JHEP11(2012)102. ArXiv:1209.1098 [hep-th]

  99. Horowitz, G.T., Santos, J.E., Tong, D.: Optical conductivity with holographic lattices. JHEP 1207, 168 (2012). doi:10.1007/JHEP07(2012)168. ArXiv:1204.0519 [hep-th]

  100. Jałmużna, J., Rostworowski, A., Bizoń, P.: A Comment on AdS collapse of a scalar field in higher dimensions. Phys. Rev. D 84, 085021 (2011). doi:10.1103/PhysRevD.84.085021. ArXiv:1108.4539 [gr-qc]

    ADS  Google Scholar 

  101. Kanti, P.: Black holes at the LHC. Lect. Notes Phys. 769, 387–423 (2009). doi:10.1007/978-3-540-88460-6_10. ArXiv:0802.2218 [hep-th]

    ADS  MathSciNet  Google Scholar 

  102. Kesden, M., Sperhake, U., Berti, E.: Final spins from the merger of precessing binary black holes. Phys. Rev. D 81, 084054 (2010). ArXiv:1002.2643 [astro-ph]

    ADS  Google Scholar 

  103. Kesden, M., Sperhake, U., Berti, E.: Relativistic suppression of black hole recoils. Astrophys. J. 715, 1006–1011 (2010). ArXiv:1003.4993 [astro-ph]

    ADS  Google Scholar 

  104. Klebanov, I.R.: TASI lectures: introduction to the AdS/CFT correspondence. pp. 615–650 (2000). Hep-th/0009139

  105. Komossa, S., Zhou, H., Lu, H.: A recoiling supermassive black hole in the quasar SDSSJ092712.65+294344.0? Astrophys. J. 678, L81 (2008). ArXiv:0804.4585 [astro-ph]

    ADS  Google Scholar 

  106. Lehner, L.: Numerical relatvity: a review. Class. Quantum Grav. 18, R25–R86 (2001). doi:10.1088/0264-9381/18/17/202. Gr-qc/0106072

    ADS  MATH  MathSciNet  Google Scholar 

  107. Lehner, L., Pretorius, F.: Black strings, low viscosity fluids, and violation of cosmic censorship. Phys. Rev. Lett. 105, 101102 (2010). doi:10.1103/PhysRevLett.105.101102. ArXiv:1006.5960 [hep-th]

    ADS  MathSciNet  Google Scholar 

  108. Li, Y., et al.: Formation of \(z\tilde{\;}6\) quasars from hierarchical galaxy mergers. Astrophys. J. 665, 187–208 (2007). Astro-ph/0608190

    ADS  Google Scholar 

  109. Lindblom, L.: Use and abuse of the model waveform accuracy standards. Phys. Rev. D 80, 064019 (2009). ArXiv:0907.0457 [gr-qc]

    ADS  Google Scholar 

  110. Lindblom, L., Baker, J.G., Owen, B.J.: Improved time-domain accuracy standards for model gravitational waveforms. Phys. Rev. D 82, 084020 (2010). ArXiv:1008.1803 [gr-qc]

    ADS  Google Scholar 

  111. MacDonald, I., Nissanke, S., Pfeiffer, H.P.: Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors. Class. Quantum Grav. 28, 134002 (2011). doi:10.1088/0264-9381/28/13/134002. ArXiv:1102.5128 [gr-qc]

    ADS  Google Scholar 

  112. Magorrian, J., Tremaine, S., Richstone, D., Bender, R., Bower, G., Dressler, A., Faber, S.M., Gebhardt, K., Green, R., Grillmair, C., Kormendy, J., Lauer, T.: The demography of massive dark objects in galaxy centers. Astron. J 115, 2285–2305 (1998). Astro-ph/9708072

    ADS  Google Scholar 

  113. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1997). Hep-th/9711200

    ADS  MathSciNet  Google Scholar 

  114. Maliborski, M., Rostworowski, A.: Time-periodic solutions in Einstein AdS—massless scalar field system. Phys. Rev. Lett. 111, 051102 (2013). doi:10.1103/PhysRevLett.111.051102. ArXiv:1303.3186 [gr-qc]

    ADS  Google Scholar 

  115. Megevand, M.: Perturbed disks get shocked. Binary black hole merger effects on accretion disks. Phys. Rev. D80, 024012 (2009). doi:10.1103/PhysRevD.80.024012. ArXiv:0905.3390 [astro-ph]

    ADS  Google Scholar 

  116. Merritt, D., Milosavljević, M., Favata, M., Hughes, S., Holz, D.: Consequences of gravitational radiation recoil. Astrophys. J. 607, L9–L12 (2004). Astro-ph/0402057

    ADS  Google Scholar 

  117. Mösta, P., et al.: Vacuum electromagnetic counterparts of binary black-hole mergers. Phys. Rev. D 81, 064017 (2010). doi:10.1103/PhysRevD.81.064017. ArXiv:0912.2330 [gr-qc]

    ADS  Google Scholar 

  118. Mroué, A.H., et al.: A catalog of 171 high-quality binary black-hole simulations for gravitational-wave astronomy. Phys. Rev. Lett. 111, 241104 (2013). ArXiv:1304.6077 [gr-qc]

    Google Scholar 

  119. Nastase, H.: Introduction to AdS-CFT (2007). Report number TIT-HEP-578. ArXiv:0712.0689 [hep-th].

  120. Okawa, H., Nakao, K.I., Shibata, M.: Is super-Planckian physics visible? Scattering of black holes in 5 dimensions. Phys. Rev. D 83, 121501 (2011). ArXiv:1105.3331 [gr-qc]

    ADS  Google Scholar 

  121. Palenzuela, C., Anderson, M., Lehner, L., Liebling, S.L., Neilsen, D.: Stirring, not shaking: binary black holes’ effects on electromagnetic fields. Phys. Rev. Lett. 103, 081101 (2009). doi:10.1103/PhysRevLett.103.081101. ArXiv:0905.1121 [astro-ph]

    ADS  Google Scholar 

  122. Palenzuela, C., Garrett, T., Lehner, L., Liebling, S.L.: Magnetospheres of black hole systems in force-free plasma. Phys. Rev. D 82, 044045 (2010). doi:10.1103/PhysRevD.82.044045. ArXiv:1007.1198 [gr-qc]

    ADS  Google Scholar 

  123. Palenzuela, C., Lehner, L., Liebling, S.L.: Dual jets from binary black holes. Science 329, 927 (2010). doi:10.1126/science.1191766. ArXiv:1005.1067 [astro-ph]

    ADS  Google Scholar 

  124. Palenzuela, C., Lehner, L., Yoshida, S.: Understanding possible electromagnetic counterparts to loud gravitational wave events: binary black hole effects on electromagnetic fields. Phys. Rev. D 81, 084007 (2010). doi:10.1103/PhysRevD.81.084007. ArXiv:0911.3889 [gr-qc]

    ADS  Google Scholar 

  125. Pan Yi. and Buonanno, A., Boyle, M., Buchman, L.T., Kidder L, E., Pfeiffer, H.P., Scheel, M.A.: Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism. Phys. Rev. D 84, 124052. doi:10.1103/PhysRevD.84.124052. ArXiv:1106.1021 [gr-qc]

  126. Pan, Y., Buonanno, A., Buchman, L.T., Chu, T., Kidder, L.E., Pfeiffer, H.P., Scheel, M.A.: Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of nonprecessing, spinning, equal-mass black holes. Phys. Rev. D 81, 084041 (2010). doi:10.1103/PhysRevD.81.084041. ArXiv:0912.3466 [gr-qc]

    ADS  Google Scholar 

  127. Pani, P., Cardoso, V., Gualtieri, L., Berti, E., Ishibashi, A.: Black hole bombs and photon mass bounds. Phys. Rev. Lett. 109, 131102 (2012). doi:10.1103/PhysRevLett.109.131102. ArXiv:1209.0465 [gr-qc]

    ADS  Google Scholar 

  128. Pekowsky, L., O’Shaughnessy, R., Healy, J., Shoemaker, D.: Comparing gravitational waves from nonprecessing and precessing black hole binaries in the corotating frame. Phys. Rev. D 88, 024040 (2013). doi:10.1103/PhysRevD.88.024040. ArXiv:1304.3176 [gr-qc]

    ADS  Google Scholar 

  129. Peres, A.: Classical radiation recoil. Phys. Rev. 128, 2471–2475 (1962)

    ADS  MATH  MathSciNet  Google Scholar 

  130. Peters, P.C.: Gravitational radiation and the motion of two point masses. Phys. Rev. 136, B1224–B1232 (1964)

    ADS  Google Scholar 

  131. Pfeiffer, H.P.: Numerical simulations of compact object binaries. Class. Quantum Grav. 29, 124004 (2012). doi:10.1088/0264-9381/29/12/124004. ArXiv:1203.5166 [gr-qc]

    ADS  Google Scholar 

  132. Pretorius, F.: Evolution of binary black-hole spacetimes. Phys. Rev. Lett. 95, 121101 (2005). doi:10.1103/PhysRevLett.95.121101. Gr-qc/0507014

    ADS  MathSciNet  Google Scholar 

  133. Pretorius, F.: Numerical relativity using a generalized harmonic decomposition. Class. Quantum Grav. 22, 425–452 (2005). doi:10.1088/0264-9381/22/2/014. Gr-qc/0407110

    ADS  MATH  MathSciNet  Google Scholar 

  134. Pretorius, F.: Binary black hole coalescence. In: Colpi, M., et al. (ed.) Physics of relativistic objects in compact binaries: from birth to coalescence. Springer, New York (2009). ArXiv:0710.1338 [gr-qc]

  135. Pretorius, F., Khurana, D.: Black hole mergers and unstable circular orbits. Class. Quantum Grav. 24, S83–S108 (2007). doi:10.1088/0264-9381/24/12/S07. Gr-qc/0702084

    ADS  MATH  MathSciNet  Google Scholar 

  136. Pürrer, M., Hannam, M., Ajith, P., Husa, S.: Testing the validity of the single-spin approximation in inspiral-merger-ringdown waveforms. Phys. Rev. D 88, 064007 (2013). doi:10.1103/PhysRevD.88.064007. ArXiv:1306.2320 [gr-qc]

    ADS  Google Scholar 

  137. Randall, L., Sundrum, R.: A large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370–3373 (1999). doi:10.1103/PhysRevLett.83.3370. Hep-ph/9905221

    ADS  MATH  MathSciNet  Google Scholar 

  138. Randall, L., Sundrum, R.: An alternative to compactification. Phys. Rev. Lett. 83, 4690–4693 (1999). doi:10.1103/PhysRevLett.83.4690. Hep-th/9906064

    ADS  MATH  MathSciNet  Google Scholar 

  139. Rees, M.J.: Accretion and the quasar phenomenon. Phys. Scr. 17, 193–200 (1978)

    ADS  Google Scholar 

  140. Rinne, O., Lindblom, L., Scheel, M.A.: Testing outer boundary treatments for the Einstein equations. Class. Quantum Grav. 24, 4053–4078 (2007). doi:10.1088/0264-9381/24/16/006. ArXiv:0704.0782 [gr-qc]

    ADS  MATH  MathSciNet  Google Scholar 

  141. Ruiz, M., Rinne, O., Sarbach, O.: Outer boundary conditions for Einstein’s field equations in harmonic coordinates. Class. Quantum Grav. 24, 6349–6378 (2007). doi:10.1088/0264-9381/24/24/012. ArXiv:0707.2797 [gr-qc]

    ADS  MATH  MathSciNet  Google Scholar 

  142. Santamaria, L.: L.: Matching post-newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries. Phys. Rev. D 82, 064016 (2010). ArXiv:1005.3306

    ADS  Google Scholar 

  143. Sasaki, M., Tagoshi, H.: Analytic black hole perturbation approach to gravitational radiation. Living Rev. Rel. 6(6) (2003). http://www.livingreviews.org/lrr-2003-6

  144. Schnittman, J.D.: Spin-orbit resonance and the evolution of compact binary systems. Phys. Rev. D 70, 124020 (2004). Astro-ph/0409174

    ADS  Google Scholar 

  145. Shibata, M., Nakamura, T.: Evolution of three-dimensional gravitational waves: harmonic slicing case. Phys. Rev. D 52, 5428–5444 (1995). doi:10.1103/PhysRevD.52.5428

    ADS  MATH  MathSciNet  Google Scholar 

  146. Shibata, M., Okawa, H., Yamamoto, T.: High-velocity collisions of two black holes. Phys. Rev. D 78, 101501(R) (2008). doi:10.1103/PhysRevD.78.101501. ArXiv:0810.4735 [gr-qc]

    ADS  Google Scholar 

  147. Shibata, M., Yoshino, H.: Bar-mode instability of rapidly spinning black hole in higher dimensions: numerical simulation in general relativity. Phys. Rev. D 81, 104035 (2010). doi:10.1103/PhysRevD.81.104035. ArXiv:1004.4970 [gr-qc]

  148. Shibata, M., Yoshino, H.: Nonaxisymmetric instability of rapidly rotating black hole in five dimensions. Phys. Rev. D 81, 021501 (2010). doi:10.1103/PhysRevD.81.021501. ArXiv:0912.3606 [gr-qc]

    ADS  Google Scholar 

  149. Sorkin, E., Oren, Y.: On Choptuik’s scaling in higher dimensions. Phys. Rev. D 71, 124005 (2005). doi:10.1103/PhysRevD.71.124005. Hep-th/0502034

    ADS  Google Scholar 

  150. Sperhake, U.: Numerical relativity in higher dimensions. Int. J. Mod. Phys. D 22, 1330005 (2013). doi:10.1142/S021827181330005X. ArXiv:1301.3772 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  151. Sperhake, U., Berti, E., Cardoso, V.: Numerical simulations of black-hole binaries and gravitational wave emission. C. R. Phys. 14, 306–317 (2013). doi:10.1016/j.crhy.2013.01.004. ArXiv:1107.2819 [gr-qc]

    ADS  Google Scholar 

  152. Sperhake, U., Berti, E., Cardoso, V., Pretorius, F.: Universality, maximum radiation and absorption in high-energy collisions of black holes with spin. Phys. Rev. Lett. 111, 041101 (2013). doi:10.1103/PhysRevLett.111.041101. ArXiv:1211.6114 [gr-qc]

    ADS  Google Scholar 

  153. Sperhake, U., Brügmann, B., Müller, D., Sopuerta, C.F.: 11-orbit inspiral of a mass ratio 4:1 black-hole binary. Class. Quantum Grav. 28, 134004 (2011). doi:10.1088/0264-9381/28/13/134004. ArXiv:1012.3173 [gr-qc]

  154. Sperhake, U., Cardoso, V., Pretorius, F., Berti, E., González, J.A.: The high-energy collision of two black holes. Phys. Rev. Lett. 101, 161101 (2008). doi:10.1103/PhysRevLett.101.161101. ArXiv:0806.1738 [gr-qc]

    ADS  Google Scholar 

  155. Sperhake, U., Cardoso, V., Pretorius, F., Berti, E., Hinderer, T., Yunes, N.: Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions. Phys. Rev. Lett. 103, 131102 (2009). doi:10.1103/PhysRevLett.103.131102. ArXiv:0907.1252 [gr-qc]

    ADS  Google Scholar 

  156. Sturani, R., et al.: Complete phenomenological gravitational waveforms from spinning coalescing binaries. J. Phys. Conf. Ser. 243, 012007 (2010). ArXiv:1005.0551 [gr-qc]

    ADS  Google Scholar 

  157. Taracchini, A.: A.: A prototype effective-one-body model for non-precessing spinning inspiral-merger-ringdown waveforms. Phys. Rev. D 86, 024011 (2012). doi:10.1103/PhysRevD.86.024011. ArXiv:1202.0790 [gr-qc]

    ADS  Google Scholar 

  158. Taracchini, A, et al.: Effective-one-body model for black-hole binaries with generic mass ratios and spins (2013). ArXiv:1311.2544 [gr-qc]

  159. van Paradijs, J.: Gamma-ray Bursts. In: American Astronomical Society Meeting Abstracts. Bulletin of the American Astronomical Society, vol. 30, pp. 1291-+ (1998). ArXiv:astro-ph/9802177.

  160. Volonteri, M., Gültekin, K., Dotti, M.: Gravitational recoil: effects on massive black hole occupation fraction over cosmic time. MNRAS 404, 2143–2150 (2010). ArXiv:1001.1743 [astro-ph]

    ADS  Google Scholar 

  161. Witek, H., Cardoso, V., Gualtieri, L., Herdeiro, C., Sperhake, U., Zilhão, M.: Head-on collisions of unequal mass black holes in \(d=5\) dimensions. Phys. Rev. D 83, 044017 (2011). ArXiv:1011.0742 [gr-qc]

    ADS  Google Scholar 

  162. Witek, H., Cardoso, V., Ishibashi, A., Sperhake, U.: Superradiant instabilities in astrophysical systems. Phys. Rev. D 87, 043513 (2013). doi:10.1103/PhysRevD.87.043513. ArXiv:1212.0551 [gr-qc]

    ADS  Google Scholar 

  163. Witek, H., Zilhão, M., Gualtieri, L., Cardoso, V., Herdeiro, C., Nerozzi, A., Sperhake, U.: Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction. Phys. Rev. D 82, 104014 (2010). doi:10.1103/PhysRevD.82.104014. ArXiv:1006.3081 [gr-qc]

    ADS  Google Scholar 

  164. Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998). Hep-th/9802150

    ADS  MATH  MathSciNet  Google Scholar 

  165. Yoshino, H., Shibata, M.: Higher-dimensional numerical relativity: current status. Prog. Theor. Phys. Suppl. 189, 269–310 (2011). doi:10.1143/PTPS.189.269

    ADS  MATH  Google Scholar 

  166. Zel’dovich, Y.B.: Pis’ma. Zh. Eksp. Teor. Fiz. 14, 270 (1971)

  167. Zel’dovich, Y.B.: Zh. Eksp. Teor. Fiz 62, 2076 (1972)

  168. Zilhão, M.: New frontiers in Numerical Relativity. Ph.D. thesis, University of Porto (2012). ArXiv:1301.1509 [gr-qc]

  169. Zilhão, M., Ansorg, M., Cardoso, V., Gualtieri, L., Herdeiro, C., Sperhake, U., Witek, H.: Higher-dimensional puncture initial data. Phys. Rev. D 84, 084039 (2011). ArXiv:1109.2149 [gr-qc]

    ADS  Google Scholar 

  170. Zilhao, M., Cardoso, V., Gualtieri, L., Herdeiro, C., Sperhake, U., Witek, H.: Dynamics of black holes in de Sitter spacetimes. Phys. Rev. D 85, 104039 (2012). doi:10.1103/PhysRevD.85.104039. ArXiv:1204.2019 [gr-qc]

    ADS  Google Scholar 

  171. Zilhao, M., Cardoso, V., Herdeiro, C., Lehner, L., Sperhake, U.: Collisions of charged black holes. Phys. Rev. D 85, 124062 (2012). doi:10.1103/PhysRevD.85.124062. ArXiv:1205.1063 [gr-qc].

  172. Zilhão, M., Cardoso, V., Herdeiro, C., Lehner, L., Sperhake, U.: Collisions of oppositely charged black holes. Phys. Rev. D 89, 044008 (2014). ArXiv:1311.6483 [gr-qc]

    Google Scholar 

  173. Zilhão, M., Witek, H., Sperhake, U., Cardoso, V., Gualtieri, L., Herdeiro, C., Nerozzi, A.: Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests. Phys. Rev. D 81, 084052 (2010). doi:10.1103/PhysRevD.81.084052. ArXiv:1001.2302 [gr-qc]

    ADS  Google Scholar 

  174. Ninja homepage: https://www.ninja-project.org/doku.php

  175. NRAR homepage: https://www.ninja-project.org/doku.php?id=nrar:home

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Acknowledgments

The author thanks Emanuele Berti, Vitor Cardoso, Pau Figueras, Leonardo Gualtieri, Carlos Herdeiro, Luis Lehner, Christian Ott, Frans Pretorius, Harvey Reall, Christian Reisswig, Carlos Sopuerta, Helvi Witek, and Miguel Zilhão for many fruitful discussions. This work was supported by the FP7-PEOPLE-2011-CIG CBHEO Grant No. 293412, the FP7-PEOPLE-2011-IRSES NRHEP Grant No. 295189, the STFC Grant No. ST/I002006/1, the XSEDE Grant No. PHY-090003 by the National Science Foundation, the Cosmos supercomputer infrastructure, part of the DiRAC HPC Facility funded by STFC and BIS, the Centro de Supercomputación de Galicia (CESGA) under Grant No. ICTS-2013-249, and the European Union’s FP7 ERC Starting Grant DyBHo-256667.

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    Ulrich Sperhake

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Sperhake, U. Numerical relativity: the role of black holes in gravitational wave physics, astrophysics and high-energy physics. Gen Relativ Gravit 46, 1689 (2014). https://doi.org/10.1007/s10714-014-1689-z

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