# Tunneling radiation of fermions from the non-stationary Kerr black hole

## TL;DR

This paper investigates fermion tunneling radiation from a dynamic Kerr black hole, deriving related equations and analyzing how the black hole's changing horizon affects radiation, temperature, and surface gravity.

## Contribution

It constructs gamma matrices and Hamilton-Jacobi equations for spin 1/2 and 3/2 fermions in a non-stationary Kerr black hole, revealing the influence of horizon dynamics on radiation properties.

## Key findings

- Tunneling rate depends on horizon dynamics.
- Surface gravity and temperature relate to horizon derivatives.
- Radiation characteristics are affected by black hole non-stationarity.

## Abstract

In this paper, the tunneling radiation of fermions with spin $1/2$ and $3/2$ from the non-stationary Kerr black hole are investigated. First, according to the Dirac equation for spin $1/2$ fermions and Rarita-Schwinger equation for spin $3/2$ fermions, we construct the corresponding gamma matrixes and the derive Hamilton-Jacobi equation for spin $1/2$ and $3/2$ fermions. Then, the tunneling behavior of fermions on the event horizon is studied. Finally, we obtain the thermodynamic properties of the non-stationary Kerr black hole. The result shows that the tunneling radiation rate, surface gravity and temperature are all related to ${\dot r_H}$ and ${r'_H}$