Abstract
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 E∼kT is modified by order unity at the horizon, and we resolve the information paradox.
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References
S W Hawking, Commun. Math. Phys. 43, 199 (1975), Erratum, ibid. 46, 206 (1976) S W Hawking, Phys. Rev. D14, 2460 (1976)
S W Hawking, Phys. Rev. D72, 084013 (2005), arXiv:hep-th/0507171
S D Mathur, Class. Quant. Grav. 26, 224001 (2009), arXiv:0909.1038 [hep-th]
J D Bekenstein, Phys. Rev. D7, 2333 (1973)
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)
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
D N Page, Phys. Rev. Lett. 71, 1291 (1993), arXiv:gr-qc/9305007
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
A Dabholkar, arXiv:hep-th/0409148
A Strominger and C Vafa, Phys. Lett. B379, 99 (1996), arXiv:hep-th/9601029
O Lunin and S D Mathur, Nucl. Phys. B610, 49 (2001), arXiv:hep-th/0105136
V Balasubramanian, J de Boer, E Keski-Vakkuri and S F Ross, Phys. Rev. D64, 064011 (2001), hep-th/0011217
J M Maldacena and L Maoz, J. High Energy Phys. 0212, 055 (2002), arXiv:hep-th/0012025
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]
V S Rychkov, J. High Energy Phys. 0601, 063 (2006), arXiv:hep-th/0512053
O Lunin and S D Mathur, Phys. Rev. Lett. 88, 211303 (2002), arXiv:hep-th/0202072
S D Mathur, Nucl. Phys. B529, 295 (1998), arXiv:hep-th/9706151
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]
V Jejjala, O Madden, S F Ross and G Titchener, Phys. Rev. D71, 124030 (2005), arXiv:hep-th/0504181
V Cardoso, O J C Dias, J L Hovdebo and R C Myers, Phys. Rev. D73, 064031 (2006), arXiv:hep-th/0512277
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]
S D Mathur, arXiv:0805.3716 [hep-th]
S D Mathur, Int. J. Mod. Phys. D18, 2215 (2009), arXiv:0905.4483 [hep-th]
Acknowledgements
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.
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MATHUR, S.D. The information paradox: Conflicts and resolutions. Pramana - J Phys 79, 1059–1073 (2012). https://doi.org/10.1007/s12043-012-0417-z
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DOI: https://doi.org/10.1007/s12043-012-0417-z