Dynamical Moving Mirrors and Black Holes

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.

37 pages, 5 figures attached, epsf, harvmac, PUPT-1430

References in corpus (1)

• A Unitary S-matrix for 2D Black Hole Formation and Evaporation

Cited by in corpus (32)

• Geometric and Renormalized Entropy in Conformal Field Theory
• An Investigation of AdS${}_2$ Backreaction and Holography
• A Possible Resolution of the Black Hole Information Puzzle
• $T\bar{T}$ deformed CFT as a non-critical string
• Non-singular four-dimensional black holes and the Jackiw-Teitelboim theory
• On CFT and Quantum Chaos
• Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation
• Soluble models in 2d dilaton gravity
• Notes on moving mirrors
• Hawking Radiation and Unitary evolution
• Black Hole Evolution
• Quantum black hole entropy and Newton constant renormalization
• On the conformal equivalence between 2D black holes and Rindler spacetime
• Quantum radiation from a partially reflecting moving mirror
• Conformally Invariant Boundary Conditions for Dilaton Gravity
• Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM
• Predictability and Semiclassical Approximation at the onset of Black Hole formation
• Moving Mirror Model of Hawking Evaporation
• Hawking Radiation from Feynman Diagrams
• Dilaton gravity with a boundary: from unitarity to black hole evaporation
• Exact solutions and critical chaos in dilaton gravity with a boundary
• Canonical Equivalence of a Generic 2D Dilaton Gravity Model and a Bosonic String Theory
• Thermodynamics of doubly charged CGHS model and D1-D5-KK black holes of IIB supergravity
• Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect
• Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation
• Radiation from a receding mirror: Unruh-DeWitt detector distinguishes a Dirac fermion from a scalar boson
• Exactly solvable charged dilaton gravity theories in two dimensions
• QUANTUM CORRECTIONS AND EXTREMAL BLACK HOLES
• Critical energy flux and mass in solvable theories of 2d dilaton gravity
• Semiclassical S-matrix and black hole entropy in dilaton gravity
• Vacuum Decay in CFT and the Riemann-Hilbert problem
• Black hole mining in the RST model