Charged Particle Tunnels from the Slowly Varying Reissner--Nordstrom Black Hole

Extending Parikh and Wilczek's work to the non-stationary black hole, we
discuss the Hawking radiation of the slowly varying Reissner--Nordstrom
black hole by considering the unfixed background spacetime and the self-gravitation interaction. The result shows that the tunnelling rate is related to both the variation of Bekenstein--Hawking entropy and the radiation spectrum deviating from the purely thermal one. This is in agreement with Parikh and Wilczek's result. Then a new method to study Hawking radiation of the non-stationary black holes is presented.