Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror

Abstract

Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [$r(w)=-iα/(\w+iα)$ and $s(w)=\w/(\w+iα)$, with $\alpha \ge 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $\alpha$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when $\alpha$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.

13 pages, no figures, version to appear in Physical Review D

References in corpus (9)

• Casimir force between partially transmitting mirrors
• Hamiltonian approach to the dynamical Casimir effect
• Notes on moving mirrors
• Quantum radiation from a partially reflecting moving mirror
• Physically Sound Hamiltonian Formulation of the Dynamical Casimir Effect
• Fluctuation-dissipation theorem and the Unruh effect of scalar and Dirac fields
• Radiation from accelerated perfect or dispersive mirrors following prescribed relativistic asymptotically inertial trajectories
• Radiation from perfect mirrors starting from rest and the black body spectrum
• Dynamical Casimir Effect and the Black Body Spectrum

Cited by in corpus (8)

• Disentangling the Black Hole Vacuum
• Dynamical Casimir effect with $\delta -{\delta }^{\prime }$ mirrors
• Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
• Particle Production by a Relativistic Semi-Transparent Mirror in 1+3D Minkowski Spacetime
• Non-thermal photons and a Fermi-Dirac spectral distribution
• Atom-field dynamics in curved spacetime
• There and Back Again: Quantum Radiation from Round-trip Flying Mirrors
• Quantum communication through a partially reflecting accelerating mirror