Dynamical Moving Mirrors and Black Holes

TL;DR

This paper models a quantum system of scalar fields interacting with a moving mirror, showing its equivalence to 2D dilaton gravity, and explores black hole formation, stability issues, and potential quantum coherence preservation mechanisms.

Contribution

It introduces a quantum mechanical model of moving mirrors linked to black hole physics, including a new stability mechanism considering quantum measurement effects.

Findings

Classical instability at high energy flux leads to mirror runaway behavior.

The model establishes a scattering relation between in-falling and out-going modes.

A proposed quantum measurement-based mechanism may restore stability and preserve coherence.

Abstract

A simple quantum mechanical model of $N$ free scalar fields interacting with a dynamical moving mirror is formulated and shown to be equivalent to two-dimensional dilaton gravity. We derive the semi-classical dynamics of this system, by including the back reaction due to the quantum radiation. We develop a hamiltonian formalism that describes the time evolution as seen by an asymptotic observer, and write a scattering equation that relates the in-falling and out-going modes at low energies. At higher incoming energy flux, however, the classical matter-mirror dynamics becomes unstable and the mirror runs off to infinity. This instability provides a useful paradigm for black hole formation and introduces an analogous information paradox. Finally, we propose a new possible mechanism for restoring the stability in the super-critical situation, while preserving quantum coherence. This mechanism is based on the notion of an effective time evolution, that takes into account the quantum mechanical effect of the measurement of the Hawking radiation on the state of the infalling matter.