On the so-called "tunnelling interpretation" of black-hole radiation from the algebraic QFT viewpoint
By Valter Moretti (U. Trento)
"Tunnelling processes" through black hole horizons have been
investigated in the framework of WKB theory, discovering an interesting
interplay with Hawking radiation. We instead  adopt the point of view
of algebraic QFT in curved spacetime. Use a suitable scaling limit
towards a Killing horizon we 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 on
opposite sides of the horizon, the quantum correlation functions appear
to have thermal nature with characteristic temperature given by
Hawking's one. The approach is valid for stationary charged rotating
non-extremal black hole and also covers the case of a Killing horizon
which just temporarily exists in some finite region. These results
provide strong support to the idea that the Hawking radiation is
actually related to phenomena associated to local Killing horizons.
Finally,  the theory is applied to the model of a $\phi^3$
self-interaction in Rindler spacetime, and renormalization counterterms
are computed, obtaining that Hawking radiation perturbatively survives
the introduction of the interaction.
 V.M., N.Pinamonti, Commun.Math.Phys. 309,295–311 (2012).
 G.Collini, V.M., N.Pinamonti, Lett.Math.Phys. 104,217–232 (2014).