Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek's work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilton--Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein--Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.