  Hawking radiation is one of the cores in modern gratitational theory. Several
articles have calculated the spectrum of Hawking radiation in Boltzmann-Gibbs
statistical mechanics. However, based on recent researches, gravitational
systems cannot be studied by the standard statistical mechanics. In this
article, we calculate the modification to the spectrum of Hawking radiation in
Tsallis statistical mechanics. We obtain the modified Stefan-Boltzmann's law
and modified power of Hawking radiation. We confirm the conclusion proposed by
Giddings, namely, the radiation should originate from the effective radius,
which extends well outside the horizon of black-hole. The lifetime of black
hole and the effect of large q are discussed as well.
