State independence for tunneling processes through Black Hole horizons and Hawking radiation

Tunneling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. In this paper we instead adopt the point of view proper of QFT in curved spacetime, namely, we shall use some scaling limit techniques in order to obtain the leading order of the correlation functions related with tunneling processess through a Killing horizon. The computation will be done with respect to a certain large class of reference states for scalar elds. In the limit of sharp localization either on the external side or on opposite sides of the horizon, the quantum correlation functions are of thermal nature, where in both cases the characteristic temperature is the Hawking one. Our approach is valid for every stationary charged rotating non extremal black hole, however, since the computation is completely local, it covers the case of a Killing horizon which just temporarily exist in some nite region too. These results give a strong support to the idea that the Hawking radiation, which is detected at future innity and needs some global structures to be dened, is actually related to a local phenomenon which holds also for geometric structures (local Killing horizons) existing just for a while