, Volume 79, Issue 5, pp 1059–1073 | Cite as

The information paradox: Conflicts and resolutions



Many relativists have been long convinced that black hole evaporation leads to information loss or remnants. String theorists have however not been too worried about the issue, largely due to a belief that the Hawking argument for information loss is flawed in its details. A recently derived inequality shows that the Hawking argument for black holes with horizon can in fact be made rigorous. What happens instead is that in string theory, black hole microstates have no horizons. Thus the evolution of radiation quanta with EkT is modified by order unity at the horizon, and we resolve the information paradox.


String theory black holes 





The author thanks all his collaborators who have, over the years, helped put together the ideas discussed here. He also thanks all the members of the black hole community for their valuable comments and discussions. This work was supported in part by DOE grant DE-FG02-91ER-40690.


  1. [1]
    S W Hawking, Commun. Math. Phys. 43, 199 (1975), Erratum, ibid. 46, 206 (1976) S W Hawking, Phys. Rev. D14, 2460 (1976)Google Scholar
  2. [2]
    S W Hawking, Phys. Rev. D72, 084013 (2005), arXiv:hep-th/0507171 MathSciNetADSGoogle Scholar
  3. [3]
    S D Mathur, Class. Quant. Grav. 26, 224001 (2009), arXiv:0909.1038 [hep-th]MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    J D Bekenstein, Phys. Rev. D7, 2333 (1973)MathSciNetADSGoogle Scholar
  5. [5]
    W Israel, Phys. Rev. 164, 1776 (1967) B Carter, Phys. Rev. Lett. 26, 331 (1971) R H Price, Phys. Rev. D5, 2439 (1972) D C Robinson, Phys. Rev. Lett. 34, 905 (1975)Google Scholar
  6. [6]
    J M Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)], arXiv:hep-th/9711200 E Witten, Adv. Theor. Math. Phys. 2, 253 (1998), hep-th/9802150 S S Gubser, I R Klebanov and A M Polyakov, Phys. Lett. B428, 105 (1998), hep-th/9802109
  7. [7]
    D N Page, Phys. Rev. Lett. 71, 1291 (1993), arXiv:gr-qc/9305007 MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. [8]
    L Susskind, arXiv:hep-th/9309145 J G Russo and L Susskind, Nucl. Phys. B437, 611 (1995), arXiv:hep-th/9405117 A Sen, Nucl. Phys. B440, 421 (1995), arXiv:hep-th/9411187 A Sen, Mod. Phys. Lett. A10, 2081 (1995), arXiv:hep-th/9504147 G T Horowitz and J Polchinski, Phys. Rev. D55, 6189 (1997), arXiv:hep-th/9612146
  9. [9]
    A Dabholkar, arXiv:hep-th/0409148
  10. [10]
    A Strominger and C Vafa, Phys. Lett. B379, 99 (1996), arXiv:hep-th/9601029 MathSciNetADSGoogle Scholar
  11. [11]
    O Lunin and S D Mathur, Nucl. Phys. B610, 49 (2001), arXiv:hep-th/0105136 MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    V Balasubramanian, J de Boer, E Keski-Vakkuri and S F Ross, Phys. Rev. D64, 064011 (2001), hep-th/0011217 ADSGoogle Scholar
  13. [13]
    J M Maldacena and L Maoz, J. High Energy Phys. 0212, 055 (2002), arXiv:hep-th/0012025 MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    O Lunin and S D Mathur, Nucl. Phys. B623, 342 (2002), arXiv:hep-th/0109154 O Lunin, J Maldacena and L Maoz, arXiv:hep-th/0212210 I Kanitscheider, K Skenderis and M Taylor, arXiv:0704.0690 [hep-th]
  15. [15]
    V S Rychkov, J. High Energy Phys. 0601, 063 (2006), arXiv:hep-th/0512053 MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    O Lunin and S D Mathur, Phys. Rev. Lett. 88, 211303 (2002), arXiv:hep-th/0202072 MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    S D Mathur, Nucl. Phys. B529, 295 (1998), arXiv:hep-th/9706151 MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    S D Mathur, A Saxena and Y K Srivastava, Nucl. Phys. B680, 415 (2004), arXiv:hep-th/ 0311092 O Lunin, J. High Energy Phys. 0404, 054 (2004), arXiv:hep-th/0404006 S Giusto, S D Mathur and A Saxena, Nucl. Phys. B701, 357 (2004), arXiv:hep-th/0405017; ibid. B710, 425 (2005), arXiv:hep-th/0406103 I Bena and N P Warner, Adv. Theor. Math. Phys. 9, 667 (2005), arXiv:hep-th/0408106 I Bena and N P Warner, Phys. Rev. D74, 066001 (2006), arXiv:hep-th/0505166 P Berglund, E G Gimon and T S Levi, J. High Energy Phys. 0606, 007 (2006), arXiv:hep-th/ 0505167 A Saxena, G Potvin, S Giusto and A W Peet, J. High Energy Phys. 0604, 010 (2006), arXiv:hep-th/0509214 I Bena, C W Wang and N P Warner, Phys. Rev. D75, 124026 (2007), arXiv:hep-th/0604110 V Balasubramanian, E G Gimon and T S Levi, J. High Energy Phys. 0801, 056 (2008), arXiv:hep-th/0606118 I Bena, C W Wang and N P Warner, J. High Energy Phys. 0611, 042 (2006), arXiv:hep-th/ 0608217 J Ford, S Giusto and A Saxena, Nucl. Phys. B790, 258 (2008), arXiv:hep-th/0612227 I Bena and N P Warner, Lect. Notes Phys. 755, 1 (2008), arXiv:hep-th/0701216 I Bena, N Bobev and N P Warner, J. High Energy Phys. 0708, 004 (2007), arXiv:0705.3641 [hep-th] E G Gimon and T S Levi, J. High Energy Phys. 0804, 098 (2008), arXiv:0706.3394 [hep-th] I Bena, C W Wang and N P Warner, J. High Energy Phys. 0807, 019 (2008), arXiv:0706.3786 [hep-th] S Giusto, S F Ross and A Saxena, J. High Energy Phys. 0712, 065 (2007), arXiv:0708.3845 [hep-th] I Bena, J de Boer, M Shigemori and N P Warner, arXiv:1107.2650 [hep-th] J de Boer, S El-Showk, I Messamah and D Van den Bleeken, J. High Energy Phys. 0905, 002 (2009), arXiv:0807.4556 [hep-th]Google Scholar
  19. [19]
    V Jejjala, O Madden, S F Ross and G Titchener, Phys. Rev. D71, 124030 (2005), arXiv:hep-th/0504181 MathSciNetADSGoogle Scholar
  20. [20]
    V Cardoso, O J C Dias, J L Hovdebo and R C Myers, Phys. Rev. D73, 064031 (2006), arXiv:hep-th/0512277 MathSciNetADSGoogle Scholar
  21. [21]
    B D Chowdhury and S D Mathur, Class. Quant. Grav. 25, 135005 (2008), arXiv:0711.4817 [hep-th]; ibid. 25, 225021 (2008), arXiv:0806.2309 [hep-th]; ibid. 26, 035006 (2009), arXiv:0810.2951 [hep-th]
  22. [22]
    S D Mathur, arXiv:0805.3716 [hep-th]
  23. [23]
    S D Mathur, Int. J. Mod. Phys. D18, 2215 (2009), arXiv:0905.4483 [hep-th]MathSciNetADSGoogle Scholar

Copyright information

© Indian Academy of Sciences 2012

Authors and Affiliations

  1. 1.Department of PhysicsThe Ohio State UniversityColumbusUSA

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