Apparent horizon and event horizon thermodynamics of a Vaidya black hole using Damour-Ruffini method

Using Damour-Ruffini method, Hawking radiation from the apparent horizon of a Vaidya black hole is calculated. The thermodynamics can be built successfully on the apparent horizon. In the meantime, when a time-dependent perturbation is given to the apparent horizon, the first law of thermodynamics can also be constructed successfully at a new supersurface near the apparent horizon. The expressions of the characteristic position and temperature are consistent with the previous results. It is concluded that the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon. These conclusions can be regarded as providing some new evidences for our previous viewpoint.