Hawking Radiation via Tunnelling from Black Holes by Using Eddington–Finkelstein Coordinates

In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunnelling effect of the black holes once again. As examples of the static and stationary black holes, we calculate the tunnelling rates of Schwarzschild and Kerr black holes. In addition, the result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s and Zhang’s recent work which adopts the Painlevè coordinates. At last, we discuss carefully the condition that the coordinates system in which we study the tunnelling process should satisfy. In our opinion, the terms of the tunnelling effect are not as strict as ones in Parikh’s paper and could be softened properly.