State Independence for Tunnelling Processes Through Black Hole Horizons and Hawking Radiation |
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Authors: | Valter?Moretti Email author" target="_blank">Nicola?PinamontiEmail author |
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Institution: | (1) Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitat Jena, Max-Wien-Platz 1, D-07743 Jena, Germany |
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Abstract: | Tunnelling processes through black hole horizons have recently been investigated in the framework of WKB theory, discovering
an interesting interplay with Hawking radiation. In this paper, we instead adopt the point of view proper of QFT in curved
spacetime, namely, we use a suitable scaling limit towards a Killing horizon to obtain the leading order of the correlation
function relevant for the tunnelling. The computation is done for a certain large class of reference quantum states for scalar
fields, including Hadamard states. In the limit of sharp localization either on the external side or on opposite sides of
the horizon, the quantum correlation functions appear to have thermal nature. In both cases the characteristic temperature
is referred to the surface gravity associated with the Killing field and thus connected with 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 exists in some finite region, too. These results provide strong
support to the idea that the Hawking radiation, which is detected at future null infinity and needs some global structures
to be defined, is actually related to a local phenomenon taking place even for local geometric structures (local Killing horizons),
existing just for a while. |
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