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

## TL;DR

This paper derives a Hamilton-Jacobi equation from Dirac and Rarita-Schwinger equations in curved spacetime to analyze quantum tunneling and radiation from charged spherically symmetric black holes, enhancing understanding of black hole thermodynamics.

## Contribution

It introduces a Hamilton-Jacobi framework based on spin 1/2 and 3/2 equations for non-stationary black holes, linking quantum tunneling to black hole thermodynamics.

## Key findings

- Hamilton-Jacobi equation derived for spin particles in curved spacetime
- Quantum tunneling analysis of charged black holes conducted
- Insights into black hole radiation and thermodynamics provided

## Abstract

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