Tunneling effect of <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{S}\mathbf{L}\left(\mathit{n}, \mathit{R}\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221415_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221415_M2.png"/></alternatives></inline-formula> Toda black hole

Abstract

The SL(<i>n</i>,<i>R</i>) 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(<i>n</i>,<i>R</i>) 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(<i>n</i>,<i>R</i>) 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(<i>n</i>,<i>R</i>) 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.