# 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 [1] 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, [2] 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.

[1] V.M., N.Pinamonti, Commun.Math.Phys. 309,295–311 (2012).

[2] G.Collini, V.M., N.Pinamonti, Lett.Math.Phys. 104,217–232 (2014).