Lorentz violation, quantum tunneling, and information conservation

Abstract：

In this paper, by introducing the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power $ (E/E_{\rm QG})^2 $ , we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordström (RN) black hole. It was determined that the LIV speeds up black hole evaporation. As a result, the induced Hawking temperature was very sensitiveto changes in the energy of the radiation particle. However, at the same energy level, it was insensitiveto changes in the charge of the radiation particle. This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity. Moreover, when the effect of the LIV was included, we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation. We also determined that black hole radiation via tunneling is an entropy conservation process, and no information loss occurred during radiation, where the interpretation of the entropy of a black hole is addressed. Finally, we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.