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Time dependent Schrödinger equation for black hole evaporation: No information loss. (English) Zbl 1343.81048

Summary: In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”.
In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution.
In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
83C57 Black holes
94A17 Measures of information, entropy
35Q41 Time-dependent Schrödinger equations and Dirac equations
81P40 Quantum coherence, entanglement, quantum correlations
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References:

[1] Hawking, S. W., Comm. Math. Phys., 43, 199 (1975)
[2] Hawking, S. W., Phys. Rev. D, 14, 2460 (1976)
[3] Hawking, S. W., Phys. Rev. D, 72, 084013 (2005)
[4] Susskind, L., The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics (2008), Little, Brown and Company
[6] Hooft, G.’t, Internat. J. Modern Phys. A, 11, 4623-4688 (1996)
[9] Parikh, M. K., Gen. Relativity Gravitation, 36, 2419 (2004), First Award in The Gravity Research Foundation Essay Competition
[10] Parikh, M. K.; Wilczek, F., Phys. Rev. Lett., 85, 5042 (2000)
[11] Zhang, B.; Cai, Q.-Y.; You, L.; Zhan, M. S., Phys. Lett. B, 675, 98 (2009)
[12] Zhang, B.; Cai, Q.-Y.; Zhan, M. S.; You, L., Ann. Phys., 326, 350 (2011)
[13] Zhang, B.; Cai, Q.-Y.; Zhan, M. S.; You, L., Europhys. Lett., 94, 20002 (2011)
[15] Zhang, B.; Cai, Q.-Y.; Zhan, M. S.; You, L.
[17] Mathur, Samir D., Internat. J. Modern Phys. D, 22, 1341016 (2013), Third Award in The Gravity Research Foundation Essay Competition
[18] Corda, C., Internat. J. Modern Phys. D, 21, 1242023 (2012), Honorable Mention in the Gravity Research Foundation Competition
[19] Corda, C., J. High Energy Phys., 08, 101 (2011)
[20] Corda, C., Eur. Phys. J. C, 73, 2665 (2013)
[21] Corda, C.; Hendi, S. H.; Katebi, R.; Schmidt, N. O., J. High Energy Phys., 06, 008 (2013)
[22] Corda, C.; Hendi, S. H.; Katebi, R.; Schmidt, N. O., Adv. High Energy Phys., 527874 (2014)
[23] Corda, C.; Hendi, S. H.; Katebi, R.; Schmidt, N. O., Adv. High Energy Phys., 530547 (2014)
[24] Bohr, N., Phil. Mag., 26, 1 (1913)
[25] Bohr, N., Phil. Mag., 26, 476 (1913)
[26] Guo, X.-K.; Cai, Q.-Y., Internat. J. Theoret. Phys., 53, 2980 (2014)
[27] Motl, L., Adv. Theor. Math. Phys., 6, 1135 (2003)
[28] York, J., Phys. Rev. D, 28, 2929 (1983)
[29] Hod, S., Gen. Relativity Gravitation, 31, 1639 (1999), Fifth Award in The Gravity Research Foundation Competition · Zbl 1081.83523
[30] Maggiore, M., Phys. Rev. Lett., 100, 141301 (2008)
[31] Bohr, N., Z. Phys., 2, 423 (1920)
[32] Corda, C., Ann. Phys., 337, 49 (2013), Definitive version with corrected typos in arXiv:1305.4529v3
[34] Roy, A. E.; Clarke, D., Astronomy: Principles and Practice (2003), PBK
[35] Banerjee, R.; Majhi, B. R., Phys. Rev. D, 79, 064024 (2009)
[36] Banerjee, R.; Majhi, B. R., Phys. Lett. B, 674, 218 (2009)
[37] Hawking, S. W., (Hawking, S. W.; Israel, W., General Relativity: An Einstein Centenary Survey (1979), Cambridge University Press) · Zbl 0424.53001
[38] Shankaranarayanan, S., Modern Phys. Lett. A, 23, 1975-1980 (2008)
[39] Zhang, J., Phys. Lett. B, 668, 353-356 (2008)
[40] Bekenstein, J. D., Lett. Nuovo Cimento, 11, 467 (1974)
[41] Sakurai, J. J., Modern Quantum Mechanics (2006), Pearson Education
[43] Adler, R. J.; Chen, P.; Santiago, D. I., Gen. Relativity Gravitation, 3, 2101-2108 (2001), Third Award in The Gravity Research Foundation Essay Competition · Zbl 1003.83020
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