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Resolving the black hole causality paradox

  • Samir D. MathurEmail author
Research Article
  • 29 Downloads

Abstract

The black hole information paradox is really a combination of two problems: the causality paradox and the entanglement problem. The causality paradox arises because in the semiclassical approximation infalling matter gets causally trapped inside its own horizon; it is therefore unable to send its information back to infinity if we disallow propagation outside the light cone. We show how the causality paradox is resolved in the fuzzball paradigm. One needs to distinguish between two kinds of Rindler spaces: (a) Rindler space obtained by choosing accelerating coordinates in Minkowski space and (b) ‘pseudo-Rindler’ space, which describes the region near the surface of a fuzzball. These two spaces differ in their vacuum fluctuations. While low energy waves propagate the same way on both spaces, infalling objects with energies \(E\gg T\) suffer an ‘entropy enhanced tunneling’ in the pseudo-Rindler spacetime (b); this leads to the nucleation of a fuzzball before the infalling object gets trapped inside a horizon.

Keywords

Black holes Information paradox String theory 

Notes

Acknowledgements

I am grateful to Borun Chowdhury, Sumit Das, A. Jevicki, Oleg Lunin, Emil Martinec, David Turton and Amitabh Virmani for helpful discussions. This work is supported in part by DOE Grant de-sc0011726, and by a Grant from the FQXi foundation.

References

  1. 1.
    Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975). [Erratum-ibid. 46, 206 (1976)]ADSCrossRefGoogle Scholar
  2. 2.
    Hawking, S.W.: Phys. Rev. D 14, 2460 (1976)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Mathur, S.D.: Class. Quant. Grav. 26, 224001 (2009). arXiv:0909.1038 [hep-th]ADSCrossRefGoogle Scholar
  4. 4.
    Maldacena, J.M.: Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]
  5. 5.
    Witten, E.: Adv. Theor. Math. Phys. 2, 253 (1998)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Phys. Lett. B 428, 105 (1998)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Lunin, O., Mathur, S.D.: AdS/CFT duality and the black hole information paradox. Nucl. Phys. B 623, 342 (2002)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Lunin, O., Maldacena, J.M., Maoz, L.: arXiv:hep-th/0212210
  9. 9.
    Jejjala, V., Madden, O., Ross, S.F., Titchener, G.: Non-supersymmetric smooth geometries and D1-D5-P bound states. Phys. Rev. D 71, 124030 (2005)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Balasubramanian, V., Gimon, E.G., Levi, T.S.: JHEP 0801, 056 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    Bena, I., Warner, N.P.: Lect. Notes Phys. 755, 1 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Cardoso, V., Dias, O.J.C., Hovdebo, J.L., Myers, R.C.: Instability of non-supersymmetric smooth geometries. Phys. Rev. D 73, 064031 (2006)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Chowdhury, B.D., Mathur, S.D.: Radiation from the non-extremal fuzzball. Class. Quant. Grav. 25, 135005 (2008)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Mathur, S.D.: arXiv:0805.3716 [hep-th]
  15. 15.
    Mathur, S.D.: Int. J. Mod. Phys. D 18, 2215 (2009). arXiv:0905.4483 [hep-th]ADSCrossRefGoogle Scholar
  16. 16.
    Kraus, P., Mathur, S .D.: Int. J. Mod. Phys. D 24(12), 1543003 (2015).  https://doi.org/10.1142/S0218271815430038 ADSCrossRefGoogle Scholar
  17. 17.
    Bena, I., Mayerson, D .R., Puhm, A., Vercnocke, B.: JHEP 1607, 031 (2016).  https://doi.org/10.1007/JHEP07(2016)031 ADSCrossRefGoogle Scholar
  18. 18.
    Almheiri, A., Marolf, D., Polchinski, J.: J. Sully and JHEP 1302, 062 (2013). arXiv:1207.3123 [hep-th]CrossRefGoogle Scholar
  19. 19.
    Mathur, S.D.: Int. J. Mod. Phys. D 25(12), 1644018 (2016).  https://doi.org/10.1142/S0218271816440181. [arXiv:1609.05222 [hep-th]]ADSCrossRefGoogle Scholar
  20. 20.
  21. 21.
  22. 22.
    Witten, E.: Nucl. Phys. B 195, 481 (1982)ADSCrossRefGoogle Scholar
  23. 23.
    Mathur, S.D.: Ann. Phys. 327, 2760 (2012).  https://doi.org/10.1016/j.aop.2012.05.001. [arXiv:1205.0776 [hep-th]ADSCrossRefGoogle Scholar
  24. 24.
    Gibbons, G.W., Warner, N.P.: Class. Quant. Grav. 31, 025016 (2014).  https://doi.org/10.1088/0264-9381/31/2/025016. arXiv:1305.0957 [hep-th]ADSCrossRefGoogle Scholar
  25. 25.
    Mathur, S.D.: Fortsch. Phys. 53, 793 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    Skenderis, K., Taylor, M.: Phys. Rept. 467, 117 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    Bena, I., Giusto, S., Martinec, E .J., Russo, R., Shigemori, M., Turton, D., Warner, N .P.: Phys. Rev. Lett. 117(20), 201601 (2016).  https://doi.org/10.1103/PhysRevLett.117.201601 ADSCrossRefGoogle Scholar
  28. 28.
  29. 29.
    Das, S.R., Jevicki, A.: Mod. Phys. Lett. A 5, 1639 (1990).  https://doi.org/10.1142/S0217732390001888 ADSCrossRefGoogle Scholar
  30. 30.
  31. 31.
    Polchinski, J.: arXiv:hep-th/9411028
  32. 32.
    Jevicki, A.: unpublishedGoogle Scholar
  33. 33.
    Karczmarek, J.L., Maldacena, J.M., Strominger, A.: JHEP 0601, 039 (2006).  https://doi.org/10.1088/1126-6708/2006/01/039. arXiv:hep-th/0411174 ADSCrossRefGoogle Scholar
  34. 34.
  35. 35.
    Garriga, J., Kanno, S., Sasaki, M., Soda, J., Vilenkin, A.: JCAP 1212, 006 (2012).  https://doi.org/10.1088/1475-7516/2012/12/006. arXiv:1208.1335 [hep-th]ADSCrossRefGoogle Scholar
  36. 36.
    Frob, M.B., Garriga, J., Kanno, S., Sasaki, M., Soda, J., Tanaka, T., Vilenkin, A.: JCAP 1404, 009 (2014).  https://doi.org/10.1088/1475-7516/2014/04/009. arXiv:1401.4137 [hep-th]ADSCrossRefGoogle Scholar
  37. 37.
    D’Eath, P.D., Payne, P.N.: Phys. Rev. D 46, 658 (1992).  https://doi.org/10.1103/PhysRevD.46.658 ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Mathur, S.D., Turton, D.: Nucl. Phys. B 884, 566 (2014).  https://doi.org/10.1016/j.nuclphysb.2014.05.012. arXiv:1306.5488 [hep-th]ADSCrossRefGoogle Scholar
  39. 39.
    Amsel, A.J., Marolf, D., Virmani, A.: JHEP 0804, 025 (2008).  https://doi.org/10.1088/1126-6708/2008/04/025. arXiv:0712.2221 [hep-th]ADSCrossRefGoogle Scholar
  40. 40.
    Hooft, G.’t.: The Holographic principle: opening lecture. arXiv:hep-th/0003004
  41. 41.
    Susskind, L., Thorlacius, L., Uglum, J.: The Stretched horizon and black hole complementarity. Phys. Rev. D 48, 3743–3761 (1993). arXiv:hep-th/9306069 ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Susskind, L.: String theory and the principles of black hole complementarity. Phys. Rev. Lett. 71, 2367–2368 (1993). arXiv:hep-th/9307168 ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Susskind, L.: The World As A Hologram. J. Math. Phys. 36, 6377 (1995). arXiv:hep-th/9409089 ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Lowe, D.A., Polchinski, J., Susskind, L., et al.: Black hole complementarity versus locality. Phys. Rev. D 52, 6997–7010 (1995). arXiv:hep-th/9506138 ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Mathur, S.D., Plumberg, C.J.: Correlations in Hawking radiation and the infall problem. JHEP 1109, 093 (2011). arXiv:1101.4899 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    Mathur, S.D.: arXiv:1506.04342 [hep-th]
  47. 47.
    Maldacena, J., Susskind, L.: Fortsch. Phys. 61, 781 (2013).  https://doi.org/10.1002/prop.201300020. arXiv:1306.0533 [hep-th]ADSCrossRefGoogle Scholar
  48. 48.
    Papadodimas, K., Raju, S.: JHEP 1310, 212 (2013).  https://doi.org/10.1007/JHEP10(2013)212. arXiv:1211.6767 [hep-th]ADSCrossRefGoogle Scholar
  49. 49.
    Giddings, S.B.: Nonviolent information transfer from black holes: a field theory parameterization arXiv:1302.2613 [hep-th]
  50. 50.
    Hawking, S.W., Perry, M.J., Strominger, A.: Phys. Rev. Lett. 116(23), 231301 (2016).  https://doi.org/10.1103/PhysRevLett.116.231301. arXiv:1601.00921 [hep-th]ADSCrossRefGoogle Scholar
  51. 51.
    Ambjorn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 93, 131301 (2004).  https://doi.org/10.1103/PhysRevLett.93.131301. arXiv:hep-th/0404156 ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Bombelli, L., Lee, J., Meyer, D., Sorkin, R.: Phys. Rev. Lett. 59, 521 (1987).  https://doi.org/10.1103/PhysRevLett.59.521 ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Mathur, S.D.: arXiv:1812.11641 [hep-th]

Copyright information

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Authors and Affiliations

  1. 1.Department of PhysicsThe Ohio State UniversityColumbusUSA

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