New Coordinates for the Evaporating Vaidya Black Hole

Drawbacks of the ingoing Eddington--Finkelstein coordinates in describing the quantum thermal properties of the evaporating Vaidya black hole are presented. A new coordinate system we proposed previously Acta Phys. Sin. 46(1997)1273 is employed. In this new coordinate system, the thermal radiation temperature of the Vaidya black hole is discussed again with the back reaction method.