Alternative Derivations of Hawking Radiation

Since the original derivation of Hawking radiation, there have been lots of alternative approaches to show the same fact that black holes emit particles as hot bodies with a temperature. These alternative methods generally rely on different conditions and physical quantities to manifest the radiation, providing various points of view of this effect in the intersection of gravity and quantum theory. This chapter presents some alternative derivations of Hawking radiation in the literature, including the tunneling, anomaly and Green's function methods. From these methods, various features of the black hole system can be seen, such as the gravitational and trace anomalies of the $(1+1)$-dimensional effective theory and the analytical continuation of the complexified spacetime.