Black hole collapse simulated by vacuum fluctuations with a moving semitransparent 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 [$r(\ensuremath{\omega})=\ensuremath{-}i\ensuremath{\alpha}/(\ensuremath{\omega}+i\ensuremath{\alpha})$ and $s(\ensuremath{\omega})=\ensuremath{\omega}/(\ensuremath{\omega}+i\ensuremath{\alpha})$, with $\ensuremath{\alpha}\ensuremath{\ge}0$], the Bogoliubov coefficients on the backside of the mirror can be computed exactly. This allows us to prove that, when $\ensuremath{\alpha}$ is very large (as in the case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a blackbody radiation), in accordance with results previously obtained in the literature. However, when $\ensuremath{\alpha}$ 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.