The Fermion Tunneling from a Slowly Varying Charged Black Hole

According to the Dirac equation and the Rarita-Schwinger equation, the Hamilton-Jacobi equation in curved space-time for the spin 1/2 and 3/2 fermions have been derived. Therefore, we find the Hamilton-Jacobi equation is a fundamental equation in the semiclassical theory. By utilizing this Hamilton-Jacobi equation, we investigate the quantum tunneling radiation from slowly varying Reissner-Nordström (R-N) black hole. The results show that the Hawking temperature do not only related to the properties of slowly varying R-N black hole, but also depended on the time. Meanwhile, it finds that the Hamilton-Jacobi equation can help people more easily and effectively calculated thermodynamic properties black hole.