摘要

Hawking radiation on the apparent horizon of a Vaidya black hole is investigated using Parikh';s tunneling method. When back-reaction of particles is neglected, precisely thermal spectrum can be obtained. Then the black hole thermodynamics can be built successfully on the apparent horizon. When a relativistic perturbation is given to the apparent horizon, similar calculation can also lead to a purely thermal spectrum, which is corresponding to a modified temperature from the former. The first law thermodynamics can also be constructed successfully at a new supersurface which has a small deviation from the apparent horizon. When the event horizon is thought as such a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be built on the event horizon. 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.