Hawking Effect Of A Dynamical Black Hole

There are two parts in this thesis. The first one is about the Hawking effect of a dynamical spherically symmetric black hole; the second one is for an axisymmetric dynamical black hole . They are described in three chapters as following:In Chapter 1, the background and meaning of the content of this thesis are introduced, the related fundamental conceptions and principles are also given. They include the four laws of black hole thermodynamics and three characteristic super-surfaces of a dynamical black hole such as Event Horizon (EH), Apparent Horizon (AH) and Timelike Limit Surface (TLS). Then the definition of surface gravity in a dynamical spherically symmetric black hole is introduced. In this chapter four methods of studying Hawking effect of a dynamical black hole are listed, i.e. radiation back-reaction method by R.Balbinot,quantum tunneling method by Parikh and Wilczek, gravitational anomaly method and Damour-Ruffini method.In Chapter 2, the Hawking effect of a dynamical spherically symmetric black hole is investigated using Damour-Ruffini method. At first, we found that it is impossible to get Hawking temperature of apparent horizon via Damour-Ruffini method. Based on previous works, the tortoise coordinate is improved. Finally, several kinds of dynamical spherically symmetric black holes are studied through the new tortoise coordinate. After tortoise coordinates transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then analytically extending the outgoing waves from outside to inside of the horizon, Hawking temperature can be obtained.In Chapter 3, the Hawking effect of an axisymmetric dynamical black hole is discussed. We still use Damour-Ruffini's method and the improved tortoise coordinate. The Hawking temperature of event horizon can also be obtained smoothly.The final results indicate that more accurate Hawking temperature can be obtained if the improved tortoise coordinates are applied.