The SL(n,R) Toda black hole is an ideal field for us to study black hole physics because of its excellentmathematical 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 onlyconsider the Hawking radiation by calculating the tunneling effect of particles with zero rest mass near theevent horizon under the four-dimensional static spherical symmetric SL(n,R) Toda black hole. In the process ofparticle tunneling through the event horizon of the black hole, due to the conservation of energy, the mass ofblack hole will be changed, which will cause the event horizon to shrink. Therefore, the reaction of tunnelingparticles 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 particlepassing through the event horizon depends on the change of the black hole entropy before and after the particleexits. Under certain conditions, our results are consistent with those of RN black holes and Schwartz blackholes, and the calculation results once again support the tunneling model proposed by Parikh and Wilczek. Thissemi-classical image shows that the new black hole radiation spectrum is not a pure heat spectrum, but there isa small deviation from the pure thermal spectrum. From the knowledge of probability theory, it can be provedthat 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 holeinformation paradox, and find that the correlation between the particles emitted from black hole can carryinformation and keep the information of black hole unchanged. The specific source of this correlation, as well asthe generation mechanism, remains to be further studied. The research on the problem about black holeinformation loss reveals that information conservation remains true when gravitational correlations amongHawking radiations are properly taken into account. Information conservation principle thus states that theHawking radiation is unitary, which shows that the dynamics of a black hole obeys the laws of quantummechanics. Since a black hole is a result of general relativity, the unitarity of a black hole definitely indicatesthe possibility of a unified gravity and quantum mechanics
