Dynamical moving mirrors and black holes

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 semi-classical model appears to become unstable and the mirror seems to accelerate forever along a trajectory that runs off to infinity. This instability provides a useful paradigm for black hole formation and introduces an analogous information paradox. Finally, we indicate a possible mechanism that may restore the stability of the system at the quantum level without destroying quantum coherence.