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(w) = −iα/(ω + iα) and s(w) = ω/(ω + iα), with α ≥ 0], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when α 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 α 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.

Fifty Years of the Dynamical Casimir Effect

“…The DCE with partially reflecting mirrors in the one-dimensional models was considered in [53,102,117,131,132,[153][154][155][156][157][158][159]. The comparison of the Dirichlet and Neumann boundary conditions in terms of the solutions to Moore's Equation (6) was performed in paper [72].…”

On horizonless temperature with an accelerating mirror

“…Notably, Moore [41], DeWitt [42], and later on, Davies and Fulling [38,39] initiated a program using field theories with external conditions, which eventually demonstrated that quantities like the expectation values of the stress-energy tensor, and the localization of particles using wave packets, can be calculated in various physical problems and used to extract significant physical consequences of the quantum fields. Indeed, there has been renewed interest [23,24,[43][44][45][46][47][48][49][50][51][52][53][54] in the moving mirror model in recent years due, in part, to claims of experimental verification of the dynamical Casimir effect [55,56]. In many of these particle production scenarios, various systems that exploit the simple mathematical set up of the (1+1)-dimensional moving mirror model have led to novel experimental designs.…”

Disentangling the black hole vacuum

“…There are some examples of different reflecting conditions in Refs. [14,15], but these cannot be directly applied here. One can come up with an equation by noting that when we reverse the boundary condition, we must get a solution of the normal wave equation.…”

“…Here W is a pure phase and not relevant in the following, and F = ^aoutA l Baxut + a( 1 ,ut((A 1)T -l ) a xut (15) will not contribute to the transition element after normal ordering. With the above it is and thus…”