Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

In curved space-time, the Hamilton–Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita–Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton–Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton–Jacobi equation. The result shows that the Hamilton–Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole.