Vacuum-purified Hawking radiation from evaporating black holes: Lessons from moving mirrors

TL;DR

This paper explores how moving mirror models can produce Hawking-like radiation that is vacuum-purified without incurring excessive energy costs, revealing a fundamental disconnect between information flux and energy in quantum field theory.

Contribution

It introduces an analytic mirror trajectory mimicking black hole evaporation, clarifies the relationship between quantum information and energy fluxes, and discusses constraints for vacuum purification.

Findings

Vacuum purification can occur without large energy costs.

A fundamental disconnection exists between information flux and energy.

An analytic mirror trajectory mimicking black hole evaporation is proposed.

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 Ref. [1]. Our motivation originates from recent discussions in Refs. [2,3] 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.