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The SL(n,R) Toda black hole is an ideal field for us to study black hole physics because of its excellent mathematical structure and high symmetry. This work is mainly to study the Hawking radiation of SL(n,R) Toda black hole and and the problem about its related black hole information loss . For simplicity, we only consider the Hawking radiation by calculating the tunneling effect of particles with zero rest mass near the event horizon under the four-dimensional static spherical symmetric SL(n,R) Toda black hole. In the process of particle tunneling through the event horizon of the black hole, due to the conservation of energy, the mass of black hole will be changed, which will cause the event horizon to shrink. Therefore, the reaction of tunneling particles to the background space-time leads to the dynamic change of spacetime metric, that is, the self-gravitational action of the particles generates the tunneling barrier. The tunneling probability of the particle passing through the event horizon depends on the change of the black hole entropy before and after the particle exits. Under certain conditions, our results are consistent with those of RN black holes and Schwartz black holes, and the calculation results once again support the tunneling model proposed by Parikh and Wilczek. This semi-classical image shows that the new black hole radiation spectrum is not a pure heat spectrum, but there is a small deviation from the pure thermal spectrum. From the knowledge of probability theory, it can be proved that there is a correlation process between non-thermal spectra. According to the Shannon entropy definition, the black hole entropy is analogous to Shannon information entropy. We calculate the SL(n,R) Toda black hole information paradox, and find that the correlation between the particles emitted from black hole can carry information and keep the information of black hole unchanged. The specific source of this correlation, as well as the generation mechanism, remains to be further studied. The research on the problem about black hole information loss reveals that information conservation remains true when gravitational correlations among Hawking radiations are properly taken into account. Information conservation principle thus states that the Hawking radiation is unitary, which shows that the dynamics of a black hole obeys the laws of quantum mechanics. Since a black hole is a result of general relativity, the unitarity of a black hole definitely indicates the possibility of a unified gravity and quantum mechanics.
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Keywords:
- Hawking radiation /
- tunneling effect /
- event horizon
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[1] Hawking S W 1975 Commun. Math. Phys. 43 199
Google Scholar
[2] Hawking S W 1976 Phys. Rev. D 14 2460
Google Scholar
[3] Almheiri A, Marolf D, Polchinski J, Sully J 2013 J. High Energy Phys. 2013 062
[4] Unruh W G, Wald R M 2017 Rep. Prog. Phys. 80 092002
Google Scholar
[5] Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042
Google Scholar
[6] Parikh M K 2004 Int. J. Mod. Phys. D 13 2355
Google Scholar
[7] Zhang J Y, Zhao Z 2006 Phys. Lett. B 638 110
Google Scholar
[8] Hemming S, Keski-Vakkuri E 2001 Phys. Rev. D 64 044006
Google Scholar
[9] Jiang Q Q, Wu S Q, Cai X 2007 Phys. Rev. D 75 064029
Google Scholar
[10] Painlevé P 1921 C. R. Acad. Sci. Paris 173 677
[11] Shankaranarayanan S, Padmanabhan T, Srinivasan K 2002 Classical Quantum Gravity 19 2671
Google Scholar
[12] Srinivasan K, Padmanabhan T 1999 Phys. Rev. D 60 24007
Google Scholar
[13] Kerner R, Mann R B 2008 Classical Quantum Gravity 25 095014
Google Scholar
[14] Kerner R, Mann R B 2008 Phys. Lett. B 665 277
Google Scholar
[15] Li R, Ren J R, Wei S W 2008 Classical Quantum Gravity 25 125016
Google Scholar
[16] Criscienzo R D, Vanzo L 2008 Europhys. Lett. 82 60001
Google Scholar
[17] Lin K, Yang S Z 2009 Int. J. Theor. Phys. 48 2061
Google Scholar
[18] Lin K, Yang S Z 2009 Phys. Rev. D 79 064035
Google Scholar
[19] Lin K, Yang S Z 2009 Phys. Lett. B 674 127
Google Scholar
[20] Lin K, Yang S Z 2011 Chin. Phys. B 20 110403
Google Scholar
[21] Lu H, Yang W 2013 Classical Quantum Gravity 30 3187
[22] Gibbons G W, Wiltshire D L 1987 Annals Phys. 167 201
[23] Lu H, Pope C N 1997 Int. J. Mod. Phys. 12 2061
Google Scholar
[24] Zhang B, Cai Q Y, You L, Zhan M S 2012 Phys. Lett. B 675 98
[25] Peng C, Yang A 2021 Phys. Rev. D 103 126020
Google Scholar
[26] Harlow D 2016 Rev. Mod. Phys. 88 15002
Google Scholar
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