Entangled pairs in evaporating black holes without event horizons

Abstract

Investigations into Hawking radiation often assume a black hole model featuring an event horizon, despite the growing consensus that such causal structures may not exist in nature. While this assumption is not crucial for deriving the local properties of radiation at future null infinity, it plays a significant role in discussions about Hawking partners -- the field modes that purify Hawking radiation. This article aims to explore the definition and fate of Hawking partners in black hole scenarios where semiclassical mass loss due to Hawking radiation is considered. Our analysis avoids the assumption of event horizons and instead focuses on collapse processes that feature a trapped region bounded by a dynamical horizon. We derive the form of the partners, accounting for the effects of back-scattering. Furthermore, using these results and mild assumptions, we find that Hawking partners cannot "leak" out of the dynamical horizon to partially purify the Hawking radiation in the regime where general relativity coexists semiclassically with quantum field theory. This finding emphasizes the necessity for new physics, such as quantum gravity, to resolve the final fate of information.