Can we observe fuzzballs or firewalls?


In the fuzzball paradigm the information paradox is resolved because the black hole is replaced by an object with no horizon. One may therefore ask if observations can distinguish a traditional hole from a fuzzball. We give arguments for why the fuzzball structure should lie close to the horizon; i.e., it should be a ‘tight’ fuzzball. We find: (a) It is very difficult to reflect quanta off the surface of such a fuzzball, mainly because geodesics starting near the horizon radius cannot escape to infinity unless their starting direction is very close to radial. (b) If infalling particles interact with the emerging radiation before they are engulfed by the horizon, then we say that we have a ‘firewall behavior’. We consider several types of interactions, but find no evidence for firewall behavior in any theory that obeys causality. (c) Photons with wavelengths larger than the black hole radius can be

scattered off the emerging radiation, but a very small fraction of the backscattered photons will be able to escape back to infinity.

A preprint version of the article is available at ArXiv.


  1. [1]

    S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].

  2. [2]

    S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].

  3. [3]

    O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].

  4. [4]

    S.D. Mathur, The Fuzzball proposal for black holes: An Elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. [6]

    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  7. [7]

    I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    S.W. Hawking, Information loss in black holes, Phys. Rev. D 72 (2005) 084013 [hep-th/0507171] [INSPIRE].

  9. [9]

    S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  10. [10]

    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  11. [11]

    S.B. Giddings, Nonviolent information transfer from black holes: A field theory parametrization, Phys. Rev. D 88 (2013) 024018 [arXiv:1302.2613] [INSPIRE].

  12. [12]

    S.W. Hawking, M.J. Perry and A. Strominger, Soft Hair on Black Holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. [14]

    S.D. Mathur and D. Turton, The flaw in the firewall argument, Nucl. Phys. B 884 (2014) 566 [arXiv:1306.5488] [INSPIRE].

  15. [15]

    H.A. Buchdahl, General Relativistic Fluid Spheres, Phys. Rev. 116 (1959) 1027 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. [16]

    S.D. Mathur, Emission rates, the correspondence principle and the information paradox, Nucl. Phys. B 529 (1998) 295 [hep-th/9706151] [INSPIRE].

  17. [17]

    G.W. Gibbons and N.P. Warner, Global structure of five-dimensional fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].

  18. [18]

    V. Cardoso and P. Pani, The observational evidence for horizons: from echoes to precision gravitational-wave physics, arXiv:1707.03021 [INSPIRE].

  19. [19]

    S.D. Mathur, Black Holes and Beyond, Annals Phys. 327 (2012) 2760 [arXiv:1205.0776] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  20. [20]

    A. Tyukov, R. Walker and N.P. Warner, Tidal Stresses and Energy Gaps in Microstate Geometries, JHEP 02 (2018) 122 [arXiv:1710.09006] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  21. [21]

    S.D. Mathur, Resolving the black hole causality paradox, arXiv:1703.03042 [INSPIRE].

  22. [22]

    S.D. Mathur, Spacetime has a “thickness”, Int. J. Mod. Phys. D 26 (2017) 1742002 [arXiv:1705.06407] [INSPIRE].

  23. [23]

    D. Marolf, private communication (2013).

  24. [24]

    S.D. Mathur, What prevents gravitational collapse in string theory?, Int. J. Mod. Phys. D 25 (2016) 1644018 [arXiv:1609.05222] [INSPIRE].

  25. [25]

    O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].

  26. [26]

    I. Bena and N.P. Warner, One ring to rule them all . . . and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  27. [27]

    S.D. Mathur and D. Turton, Oscillating supertubes and neutral rotating black hole microstates, JHEP 04 (2014) 072 [arXiv:1310.1354] [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    V. Cardoso, O.J.C. Dias, J.L. Hovdebo and R.C. Myers, Instability of non-supersymmetric smooth geometries, Phys. Rev. D 73 (2006) 064031 [hep-th/0512277] [INSPIRE].

  29. [29]

    B.D. Chowdhury and S.D. Mathur, Radiation from the non-extremal fuzzball, Class. Quant. Grav. 25 (2008) 135005 [arXiv:0711.4817] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  30. [30]

    B.D. Chowdhury and S.D. Mathur, Pair creation in non-extremal fuzzball geometries, Class. Quant. Grav. 25 (2008) 225021 [arXiv:0806.2309] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  31. [31]

    B.D. Chowdhury and S.D. Mathur, Non-extremal fuzzballs and ergoregion emission, Class. Quant. Grav. 26 (2009) 035006 [arXiv:0810.2951] [INSPIRE].

  32. [32]

    V. Cardoso, E. Franzin and P. Pani, Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett. 116 (2016) 171101 [Erratum ibid. 117 (2016) 089902] [arXiv:1602.07309] [INSPIRE].

  33. [33]

    K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

  35. [35]

    L. Susskind, String theory and the principles of black hole complementarity, Phys. Rev. Lett. 71 (1993) 2367 [hep-th/9307168] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  36. [36]

    G. ’t Hooft, The Holographic principle: Opening lecture, Subnucl. Ser. 37 (2001) 72 [hep-th/0003004] [INSPIRE].

  37. [37]

    S.D. Mathur, A model with no firewall, arXiv:1506.04342 [INSPIRE].

  38. [38]

    S.D. Mathur and C.J. Plumberg, Correlations in Hawking radiation and the infall problem, JHEP 09 (2011) 093 [arXiv:1101.4899] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  39. [39]

    S.D. Mathur, Tunneling into fuzzball states, Gen. Rel. Grav. 42 (2010) 113 [arXiv:0805.3716] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  40. [40]

    S.D. Mathur, How fast can a black hole release its information?, Int. J. Mod. Phys. D 18 (2009) 2215 [arXiv:0905.4483] [INSPIRE].

  41. [41]

    P. Kraus and S.D. Mathur, Nature abhors a horizon, Int. J. Mod. Phys. D 24 (2015) 1543003 [arXiv:1505.05078] [INSPIRE].

  42. [42]

    I. Bena, D.R. Mayerson, A. Puhm and B. Vercnocke, Tunneling into Microstate Geometries: Quantum Effects Stop Gravitational Collapse, JHEP 07 (2016) 031 [arXiv:1512.05376] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  43. [43]

    A.J. Amsel, D. Marolf and A. Virmani, Collisions with Black Holes and Deconfined Plasmas, JHEP 04 (2008) 025 [arXiv:0712.2221] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  44. [44]

    T. Banks and W. Fischler, A Model for high-energy scattering in quantum gravity, hep-th/9906038 [INSPIRE].

  45. [45]

    W.G. Unruh, Absorption Cross-Section of Small Black Holes, Phys. Rev. D 14 (1976) 3251 [INSPIRE].

  46. [46]

    D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].

  47. [47]

    S.R. Das, G.W. Gibbons and S.D. Mathur, Universality of low-energy absorption cross-sections for black holes, Phys. Rev. Lett. 78 (1997) 417 [hep-th/9609052] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    V. Cardoso, S. Hopper, C.F.B. Macedo, C. Palenzuela and P. Pani, Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D 94 (2016) 084031 [arXiv:1608.08637] [INSPIRE].

  49. [49]

    J. Abedi, H. Dykaar and N. Afshordi, Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons, Phys. Rev. D 96 (2017) 082004 [arXiv:1612.00266] [INSPIRE].

  50. [50]

    T. Hertog and J. Hartle, Observational Implications of Fuzzball Formation, arXiv:1704.02123 [INSPIRE].

  51. [51]

    U.-L. Pen and A.E. Broderick, Possible Astrophysical Observables of Quantum Gravity Effects near Black Holes, Mon. Not. Roy. Astron. Soc. 445 (2014) 3370 [arXiv:1312.4017] [INSPIRE].

    ADS  Article  Google Scholar 

Download references

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.

Author information



Corresponding author

Correspondence to Shaun Hampton.

Additional information

ArXiv ePrint: 1711.01617

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Guo, B., Hampton, S. & Mathur, S.D. Can we observe fuzzballs or firewalls?. J. High Energ. Phys. 2018, 162 (2018).

Download citation


  • Black Holes
  • Black Holes in String Theory
  • Models of Quantum Gravity