Further evidence for the weak gravity — cosmic censorship connection

  • Gary T. HorowitzEmail author
  • Jorge E. Santos
Open Access
Regular Article - Theoretical Physics


We have recently shown that a class of counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime is removed if the weak gravity conjecture holds. Surprisingly, the minimum value of the charge to mass ratio necessary to preserve cosmic censorship is precisely the weak gravity bound. To further explore this mysterious connection, we investigate two generalizations: adding a dilaton or an additional Maxwell field. Analogous counterexamples to cosmic censorship are found in these theories if there is no charged matter. Even though the weak gravity bound is modified, we show that in each case it is sufficient to remove these counterexamples. In most cases it is also necessary.


Classical Theories of Gravity Spacetime Singularities Black Holes in String Theory AdS-CFT Correspondence 


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]
    G.T. Horowitz, J.E. Santos and B. Way, Evidence for an electrifying violation of cosmic censorship, Class. Quant. Grav. 33 (2016) 195007 [arXiv:1604.06465] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    T. Crisford and J.E. Santos, Violating the weak cosmic censorship conjecture in four-dimensional Anti-de Sitter space, Phys. Rev. Lett. 118 (2017) 181101 [arXiv:1702.05490] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C. Vafa, private communication.Google Scholar
  4. [4]
    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    T. Crisford, G.T. Horowitz and J.E. Santos, Testing the weak gravitycosmic censorship connection, Phys. Rev. D 97 (2018) 066005 [arXiv:1709.07880] [INSPIRE].
  6. [6]
    G.W. Gibbons and K.-i. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].
  7. [7]
    D. Garfinkle, G.T. Horowitz and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43 (1991) 3140 [Erratum ibid. D 45 (1992) 3888] [INSPIRE].
  8. [8]
    B. Heidenreich, M. Reece and T. Rudelius, Sharpening the weak gravity conjecture with dimensional reduction, JHEP 02 (2016) 140 [arXiv:1509.06374] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    C. Cheung and G.N. Remmen, Naturalness and the weak gravity conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
  10. [10]
    G.T. Horowitz, N. Iqbal, J.E. Santos and B. Way, Hovering black holes from charged defects, Class. Quant. Grav. 32 (2015) 105001 [arXiv:1412.1830] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    A.A. Starobinskil and S.M. Churilov, Amplification of electromagnetic and gravitational waves scattered by a rotatingblack hole”, Sov. Phys. JETP 65 (1974) 1.Google Scholar
  12. [12]
    G.W. Gibbons, Vacuum polarization and the spontaneous loss of charge by black holes, Commun. Math. Phys. 44 (1975) 245 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    P. Basu et al., Small hairy black holes in global AdS spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small hairy black holes in AdS 5 × S 5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
  15. [15]
    O.J.C. Dias et al., Hairy black holes and solitons in global AdS 5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].
  16. [16]
    S.A. Gentle, M. Rangamani and B. Withers, A soliton menagerie in AdS, JHEP 05 (2012) 106 [arXiv:1112.3979] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Markeviciute and J.E. Santos, Hairy black holes in AdS 5 × S 5, JHEP 06 (2016) 096 [arXiv:1602.03893] [INSPIRE].
  18. [18]
    P. Bosch, S.R. Green and L. Lehner, Nonlinear evolution and final fate of charged Anti-de Sitter black hole superradiant instability, Phys. Rev. Lett. 116 (2016) 141102 [arXiv:1601.01384] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    O.J.C. Dias and R. Masachs, Hairy black holes and the endpoint of AdS 4 charged superradiance, JHEP 02 (2017) 128 [arXiv:1610.03496] [INSPIRE].
  20. [20]
    T. Crisford, G.T. Horowitz and J.E. Santos, Attempts at vacuum counterexamples to cosmic censorship in AdS, JHEP 02 (2019) 092 [arXiv:1805.06469] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    C.F.E. Holzhey and F. Wilczek, Black holes as elementary particles, Nucl. Phys. B 380 (1992) 447 [hep-th/9202014] [INSPIRE].
  22. [22]
    G.W. Gibbons, G.T. Horowitz and P.K. Townsend, Higher dimensional resolution of dilatonic black hole singularities, Class. Quant. Grav. 12 (1995) 297 [hep-th/9410073] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    J. Markevičiutė and J.E. Santos, Stirring a black hole, JHEP 02 (2018) 060 [arXiv:1712.07648] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
  25. [25]
    A. Adam, S. Kitchen and T. Wiseman, A numerical approach to finding general stationary vacuum black holes, Class. Quant. Grav. 29 (2012) 165002 [arXiv:1105.6347] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    T. Wiseman, Numerical construction of static and stationary black holes, in Black holes in higher dimensions, G.T. Horowitz ed., Cambridge University Press, Cambridge U.K. (2012), arXiv:1107.5513 [INSPIRE].
  27. [27]
    O.J.C. Dias, J.E. Santos and B. Way, Numerical methods for finding stationary gravitational solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav. 28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    P. Figueras and T. Wiseman, On the existence of stationary Ricci solitons, Class. Quant. Grav. 34 (2017) 145007 [arXiv:1610.06178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.

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