Abstract
Are there any degrees of freedom on the black hole horizon? Using the ‘membrane paradigm’ we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need ‘real’ degrees of freedom at the horizon, which can modify Hawking’s evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.
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References
Bekenstein J.D.: Phys. Rev. D 7, 2333 (1973)
Bekenstein J.D.: Lett. Nuovo Cim. 11, 467 (1974)
Rovelli, C., Smolin, L.: Nucl. Phys. B 442, 593 (1995). arXiv:gr-qc/9411005 [Erratum-ibid. B 456, 753 (1995)]
Thorne K.S., Price R.H., Macdonald D.A.: The Membrane Paradigm, pp. 367. Yale University Press, New Haven, USA (1986)
Susskind L., Thorlacius L., Uglum J.: Phys. Rev. D 48, 3743 (1993) arXiv:hep-th/9306069
Sciama D.W., Candelas P., Deutsch D.: Adv. Phys. 30, 327 (1981)
Hawking S.W.: Commun. Math. Phys. 43, 199 (1975) [Erratum-ibid. 46, 206 (1976)]
Hawking S.W.: Phys. Rev. D 14, 2460 (1976)
Mathur S.D.: Class. Quant. Grav. 26, 224001 (2009) arXiv:0909.1038 [hep-th]
Lieb E.H., Ruskai M.B.: J. Math. Phys. 14, 1938 (1973)
Lunin O., Mathur S.D.: Nucl. Phys. B 623, 342 (2002) arXiv:hep-th/0109154
Lunin O., Mathur S.D.: Phys. Rev. Lett. 88, 211303 (2002) arXiv:hep- th/0202072
Lunin, O., Maldacena, J.M., Maoz, L.: arXiv:hep-th/0212210
Kanitscheider, I., Skenderis, K., Taylor, M.: JHEP 0706, 056 (2007). arXiv:0704.0690 [hep-th]
Giusto S., Mathur S.D., Saxena A.: Nucl. Phys. B 710, 425 (2005) arXiv:hep-th/0406103
Bena I., Warner N.P.: Adv. Theor. Math. Phys. 9, 667 (2005) arXiv:hep-th/0408106
Jejjala V., Madden O., Ross S.F., Titchener G.: Phys. Rev. D 71, 124030 (2005) arXiv:hep-th/0504181
Balasubramanian, V., Gimon, E.G., Levi, T.S.: arXiv:hep-th/0606118
de Boer J., Denef F., El-Showk S., Messamah I., Vanden Bleeken D.: JHEP 0811, 050 (2008) arXiv:0802.2257 [hep-th]
Mathur S.D.: arXiv:0810.4525 [hep-th]
Mathur, S.D.: arXiv:0706.3884 [hep-th]
Cardoso V., Dias O.J.C., Hovdebo J.L., Myers R.C.: Phys. Rev. D 73, 064031 (2006) arXiv:hep-th/0512277
Chowdhury B.D., Mathur S.D.: Class. Quant. Grav. 25, 135005 (2008) arXiv:0711.4817 [hep-th]
Mathur, S.D.: arXiv:0805.3716 [hep-th]
Mathur S.D.: Int. J. Mod. Phys. D 18, 2215 (2009) arXiv:0905.4483 [hep-th]
Hayden P., Preskill J.: JHEP 0709, 120 (2007) arXiv:0708.4025 [hep-th]
Sekino Y., Susskind L.: JHEP 0810, 065 (2008) arXiv:0808.2096 [hep-th]
Maldacena J.M.: Adv. Theor. Math. Phys. 2, 231 (1998)
Maldacena J.M.: Int. J. Theor. Phys. 38, 1113 (1999) arXiv:hep-th/9711200
Parikh M., Wilczek F.: Phys. Rev. D 58, 064011 (1998) arXiv:gr-qc/9712077
Shimomura T., Okamura T., Mishima T.: Int. J. Mod. Phys. D 11, 789 (2002)
Kovtun P., Son D.T., Starinets A.O.: JHEP 0310, 064 (2003) arXiv:hep-th/0309213
Cardoso V., Dias O.J.C., Gualtieri L.: Int. J. Mod. Phys. D 17, 505 (2008) arXiv:0705.2777 [hep-th]
Natsuume M.: Phys. Rev. D 78, 066010 (2008) arXiv:0807.1392 [hep-th]
IqbalN. Liu H.: Phys. Rev. D 79, 025023 (2009) arXiv:0809.3808 [hep-th]
Culetu, H.: arXiv:0906.0920 [gr-qc]
Eling C., Oz Y.: JHEP 1002, 069 (2010) arXiv:0906.4999 [hep-th]
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Second Award in the 2010 Essay Competition of the Gravity Research Foundation.
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Mathur, S.D. Membrane paradigm realized?. Gen Relativ Gravit 42, 2331–2336 (2010). https://doi.org/10.1007/s10714-010-1022-4
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DOI: https://doi.org/10.1007/s10714-010-1022-4