State independence for tunneling processes through black hole horizons and Hawking radiation

TL;DR

This paper uses quantum field theory techniques to show that Hawking radiation can be understood as a local phenomenon near black hole horizons, independent of global spacetime structures.

Contribution

It introduces a local scaling limit approach to analyze tunneling and Hawking radiation, applicable to a broad class of stationary black holes and even temporary Killing horizons.

Findings

Quantum correlations near horizons exhibit thermal, Hawking-like temperature.

The approach is valid for stationary charged rotating non-extremal black holes.

Hawking radiation can originate from local geometric structures, not just global spacetime features.

Abstract

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 use a suitable scaling limit technique to obtain the leading order of the correlation function related with some tunneling process through a Killing horizon. The computation is done for certain large class of reference quantum states for scalar fields. 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, 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 exists in some finite region too. These results give a strong support to the idea that the Hawking radiation, which is detected at future 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.