Lorentz-violating theory and tunneling radiation characteristics of Dirac particles in curved spacetime of Vaidya black hole

In this paper, the modified Hawking radiation for Dirac particles via tunneling from the apparent horizon of Vaidya black hole is studied by using the Lorentz-violating Dirac field theory. We first extend the gamma matric from flat spacetime to the curved spacetime in the Lorentz-violating Dirac field theory, and generalize the general derivative to the covariant derivative. Then, by considering the commutative relation of the gamma matric, the Dirac equation in the Lorentz-violating Dirac field theory is obtained, which contains three correction terms related to the Lorentz-symmetry violation. In the semiclassical approximation, the modified Hamilton-Jacobi equation is obtained by using the commutative relation of gamma matric and treating the aether-like vector in the Lorentz-violating theory as a constant. We find that the modified Hamilton-Jacobi equation contains only two correction terms based on the Lorentz-symmetry violation, i.e. the corrected term containing the parameter a affects the mass term of the Dirac field, and the aether-like term containing the parameter c modifies the coefficient term of the action S of the separating variable. According to the modified Hamilton-Jacobi equation, we study the effect of Lorentz-symmetry violation on the characteristics of Hawking radiation for Dirac particles via tunneling from the apparent horizon r(a) = 2M(v) of Vaidya black hole (the apparent horizon of Vaidya black hole coincides with the timelike limit surface, so the apparent horizon can be regarded as the boundary of Vaidya black hole). Since the Hawking tunneling radiation of black holes is the radial property at the horizon of black holes, we finally find that only the aether-like term containing the parameter c can modify the characteristics of Dirac particles' tunneling radiation from the black hole. In addition, the corrected Hawking temperature of the black hole caused by considering the effect on the Lorentz-violating Dirac field theory has a small correction related to the aether-like term, which is consistent with the results obtained by studying the characteristics of Hawking tunneling radiation for scalar particles in the Lorentz-violating scalar field theory. The results suggest that the Lorentz-symmetry violation theory may provide a new method to further study the information loss paradox of black holes.