Tunneling effect of SL(n,R) Toda black hole

Since the SL(n,R) Toda black hole has a very good mathematical structure and high symmetry, it is an ideal field for us to study black hole physics. This paper mainly studies the Hawking radiation of SL(n,R) Toda black hole and its related black hole information loss paradox. For simplicity, we only consider the study of 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 causes 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 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 spectrum. By using the Shannon entropy definition, the black hole entropy is analogous to Shannon information entropy. We have calculated the SL(n,R) Toda black hole information paradox, and found that the correlation between black hole radiation particles can carry information and maintain the conservation of black hole information. The specific source of this association, as well as the generation mechanism, remains to be further studied. The research on black hole information loss problem reveals that information conservation remains true when gravitational correlations among Hawking radiations are properly taken into account. Information conservation principle thus states Hawking radiation is unitary, which shows that the dynamics of a black hole obey 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.