Journal of High Energy Physics

, 2019:99 | Cite as

Black hole collisions, instabilities, and cosmic censorship violation at large D

  • Tomás Andrade
  • Roberto EmparanEmail author
  • David Licht
  • Raimon Luna
Open Access
Regular Article - Theoretical Physics


We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evidence that they lead to violations of cosmic censorship. The post-merger evolution of the collision of two black holes with total angular momentum above a certain value is governed by the properties of a resonance-like intermediate state: a long-lived, rotating black bar, which pinches off towards a naked singularity due to an instability akin to that of black strings. We compute the radiative loss of spin for a rotating bar using the quadrupole formula at finite D, and argue that at large enough D — very likely for D ≳ 8, but possibly down to D = 6 — the spin-down is too inefficient to quench this instability. We also study the instabilities of ultraspinning black holes by solving numerically the time evolution of axisymmetric and non-axisymmetric perturbations. We demonstrate the development of transient black rings in the former case, and of multi-pronged horizons in the latter, which then proceed to pinch and, arguably, fragment into smaller black holes.


Black Holes Spacetime Singularities 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


  1. [1]
    T. Andrade, R. Emparan, D. Licht and R. Luna, Cosmic censorship violation in black hole collisions in higher dimensions, JHEP 04 (2019) 121 [arXiv:1812.05017] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Andrade, R. Emparan and D. Licht, Rotating black holes and black bars at large D, JHEP 09 (2018) 107 [arXiv:1807.01131] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    R. Penrose, Gravitational collapse: the role of general relativity, Riv. Nuovo Cim. 1 (1969) 252 [Gen. Rel. Grav. 34 (2002) 1141] [INSPIRE].
  4. [4]
    R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Shibata and H. Yoshino, Bar-mode instability of rapidly spinning black hole in higher dimensions: numerical simulation in general relativity, Phys. Rev. D 81 (2010) 104035 [arXiv:1004.4970] [INSPIRE].
  7. [7]
    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    L. Lehner and F. Pretorius, Black strings, low viscosity fluids and violation of cosmic censorship, Phys. Rev. Lett. 105 (2010) 101102 [arXiv:1006.5960] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    V. Cardoso, O.J.C. Dias and J.P.S. Lemos, Gravitational radiation in D-dimensional space-times, Phys. Rev. D 67 (2003) 064026 [hep-th/0212168] [INSPIRE].
  10. [10]
    H. Bantilan, P. Figueras, M. Kunesch and R. Panosso Macedo, The end point of nonaxisymmetric black hole instabilities in higher dimensions, arXiv:1906.10696 [INSPIRE].
  11. [11]
    T. Andrade, R. Emparan and D. Licht, Charged rotating black holes in higher dimensions, JHEP 02 (2019) 076 [arXiv:1810.06993] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    R. Emparan, R. Suzuki and K. Tanabe, Evolution and end point of the black string instability: large D solution, Phys. Rev. Lett. 115 (2015) 091102 [arXiv:1506.06772] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    R. Emparan et al., Hydro-elastic complementarity in black branes at large D, JHEP 06 (2016) 117 [arXiv:1602.05752] [INSPIRE].
  14. [14]
    R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
  16. [16]
    M.M. Caldarelli, J. Camps, B. Goutéraux and K. Skenderis, AdS/Ricci-flat correspondence and the Gregory-Laflamme instability, Phys. Rev. D 87 (2013) 061502 [arXiv:1211.2815] [INSPIRE].
  17. [17]
    C.P. Herzog, M. Spillane and A. Yarom, The holographic dual of a Riemann problem in a large number of dimensions, JHEP 08 (2016) 120 [arXiv:1605.01404] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Y. Dandekar et al., The large D black hole membrane paradigm at first subleading order, JHEP 12 (2016) 113 [arXiv:1607.06475] [INSPIRE].
  19. [19]
    S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [INSPIRE].
  20. [20]
    O.J.C. Dias et al., Instability and new phases of higher-dimensional rotating black holes, Phys. Rev. D 80 (2009) 111701 [arXiv:0907.2248] [INSPIRE].
  21. [21]
    R. Suzuki and K. Tanabe, Stationary black holes: large D analysis, JHEP 09 (2015) 193 [arXiv:1505.01282] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    O.J.C. Dias, J.E. Santos and B. Way, Rings, ripples and rotation: connecting black holes to black rings, JHEP 07 (2014) 045 [arXiv:1402.6345] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    R. Emparan, P. Figueras and M. Martinez, Bumpy black holes, JHEP 12 (2014) 072 [arXiv:1410.4764] [INSPIRE].
  24. [24]
    R. Emparan and R. Suzuki, Topology-changing horizons at large D as Ricci flows, JHEP 07 (2019) 094 [arXiv:1905.01062] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    P. Figueras, M. Kunesch, L. Lehner and S. Tunyasuvunakool, End point of the ultraspinning instability and violation of cosmic censorship, Phys. Rev. Lett. 118 (2017) 151103 [arXiv:1702.01755] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    P. Figueras, M. Kunesch and S. Tunyasuvunakool, End point of black ring instabilities and the weak cosmic censorship conjecture, Phys. Rev. Lett. 116 (2016) 071102 [arXiv:1512.04532] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    E. Sorkin, A critical dimension in the black string phase transition, Phys. Rev. Lett. 93 (2004) 031601 [hep-th/0402216] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    R. Emparan et al., Phases and stability of non-uniform black strings, JHEP 05 (2018) 104 [arXiv:1802.08191] [INSPIRE].
  30. [30]
    H. Yoshino and Y. Nambu, Black hole formation in the grazing collision of high-energy particles, Phys. Rev. D 67 (2003) 024009 [gr-qc/0209003] [INSPIRE].
  31. [31]
    H. Yoshino and V.S. Rychkov, Improved analysis of black hole formation in high-energy particle collisions, Phys. Rev. D 71 (2005) 104028 [Erratum ibid. D 77 (2008) 089905] [hep-th/0503171] [INSPIRE].
  32. [32]
    M. Shibata, H. Okawa and T. Yamamoto, High-velocity collision of two black holes, Phys. Rev. D 78 (2008) 101501 [arXiv:0810.4735] [INSPIRE].
  33. [33]
    U. Sperhake et al., The high-energy collision of two black holes, Phys. Rev. Lett. 101 (2008) 161101 [arXiv:0806.1738] [INSPIRE].
  34. [34]
    F.S. Coelho, C. Herdeiro and M.O.P. Sampaio, Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula, Phys. Rev. Lett. 108 (2012) 181102 [arXiv:1203.5355] [INSPIRE].
  35. [35]
    W.E. East and F. Pretorius, Ultrarelativistic black hole formation, Phys. Rev. Lett. 110 (2013) 101101 [arXiv:1210.0443] [INSPIRE].
  36. [36]
    J. Bezanson, A. Edelman, S. Karpinski and V.B. Shah, JuliaA fresh approach to numerical computing, SIAM review 59 (2017) 65.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
  38. [38]
    C. Rackauckas and Q. Nie, DifferentialEquations.jlA performant and feature-rich ecosystem for solving differential equations in Julia, JORS 5 (2017) 15.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Departament de F ısica Quàntica i Astrof´ısica, Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

Personalised recommendations