Perturbative quantum consistency near black-hole horizon formation

TL;DR

This paper investigates the quantum behavior near black-hole horizon formation using a physical shell model, deriving a propagator that links interior and exterior regions, and analyzing vacuum stability during collapse.

Contribution

It provides the first derivation of a Feynman propagator connecting interior and exterior regions during near-horizon collapse, ensuring perturbative unitarity.

Findings

The propagator accurately describes quantum fields across the shell interface.

Vacuum persistence amplitude remains consistent with unitarity on short timescales.

Results support the perturbative consistency of quantum fields near horizon formation.

Abstract

We study the prelude to black-hole formation using a suspended shell composed of physical matter that fulfills the dominant energy condition. Here, the collapse of the shell is brought to rest when the formation of the horizon is imminent but has not yet occurred. As the main achievement of this work, we obtain the Feynman propagator which connects the interior and the exterior of the shell within two local coordinate patches. It is derived by drawing an analogy to the propagation of light across interfaces that separate regions with different susceptibilities inside a medium. As a first application, we use this propagator to determine the vacuum persistence amplitude in the presence of external sources. On timescales much shorter than the Page time, we find that the amplitude builds up with time yet remains consistent with perturbative unitarity.