Vacuum-purified Hawking radiation from evaporating black holes: Lessons from moving mirrors
Phys. Rev. D 113, 085010 – Published 13 April, 2026
DOI: https://doi.org/10.1103/spl3-5qmr
Abstract
This article investigates the possibility that Hawking-like quanta emitted by a moving mirror can be purified by late-time vacuum fluctuations, as proposed in Hotta, Schützhold and Unruh [Phys. Rev. D 91, 124060 (2015)]. Our motivation originates from recent discussions in Wald [Phys. Rev. D 100, 065019 (2019)] and Osawa et al. [Phys. Rev. D 110, 025023 (2024)] on whether vacuum purification necessarily entails a prohibitively large (indirect) energy cost, and our goal is to help clarify this issue. We identify the aspects of the mirror trajectory that determine the partners of Hawking quanta, as well as those that govern the energy carried to future null infinity. This allows us to highlight a fundamental disconnection within quantum field theory between the fluxes of quantum information (or purification) and energy. Throughout, we focus on quantities such as local correlation functions and energy fluxes, thereby avoiding reliance on a particle-based interpretation. Finally, we introduce an analytic mirror trajectory that produces Hawking radiation with an adiabatically varying temperature, mimicking the emission from an evaporating black hole. Our analysis identifies constraints on the mirror trajectory under which vacuum purification remains compatible with a prescribed energy budget, and we discuss the lessons that may be drawn from this model for realistic evaporating black holes.
