Charged particle tunnels from the stationary and non-stationary Kerr–Newman black holes

Considering the unfixed background space-time and self-gravitational interaction, we view the Hawking radiation of a stationary Kerr-Newman black hole by Hamilton-Jacobi method. Meanwhile, extending this work to non-stationary black holes, we attempt to investigate the Hawking radiation of the non-stationary Kerr-Newman black hole. Both of the results show the tunneling probabilities are related to the change of Bekenstein- Hawking entropy and the radiation spectrums deviate from the purely thermal one, which is in accordance with the known result.