Correction of Lorentz breaking theory to quantum tunneling radiation and entropy of black hole in gravity's rainbow

Considering the Lorentz breaking theory, the correct modified forms of the dynamic equations of bosons and fermions in curved space-time are studied. For the new form of fermions dynamic equation through spin 1/2 Dirac particles in the black hole space-time in gravity's rainbow, by introducing aether-like vector field and correctly constructing gamma matrix, new meaningful expressions of Hawking temperature, tunneling rate and Bekenstein-Hawking entropy of this black hole are obtained. In addition, the distribution characteristics of the energy levels of Dirac particles are also studied, and meaningful results are obtained. The research results show that the Lorentz breaking terms will cause a certain degree of correction to the tunneling radiation of fermions in the curved space-time of the black hole.