Hawking radiation far away from the event horizon

We study particle production in Vaidya spacetime. Using the WKB approximation, the distribution of Hawking radiation is calculated without the near-horizon approximation, which leads to finite corrections to the purely thermal spectrum. We extend our analysis to extremal and non-extremal Reissner-Nordstr\"om and Kerr black holes. Our results can be understood in terms of a thermodynamic toy model, where one regards Hawking radiation as Unruh radiation perceived by observers outside of the black hole. Moreover, we extend the model to incorporate the backreaction of Hawking quanta on spacetime geometry. Our study suggests that the backreaction may prevent the formation of the event horizon and spacetime singularity.