Action of the gravitational field on the dynamical Casimir effect

Abstract

In this paper we analyze the action of the gravitational field on the dynamical Casimir effect.We consider a massless scalar field confined in a cuboid cavity placed in a gravitational field described by a static and diagonal metric. With one of the plane mirrors of the cavity allowed to move, we compute the average number of particles created inside the cavity by means of the Bogoliubov coefficients computed through perturbative expansions. We apply our result to the case of an oscillatory motion of the mirror, assuming a weak gravitational field described by the Schwarzschild metric. The regime of parametric amplification is analyzed in detail, demonstrating that our computed result for the mean number of particles created agrees with specific associated cases in the literature. Our results, obtained in the framework of the perturbation theory, are restricted, under resonant conditions, to a short-time limit.

Dynamical Casimir effect in curved spacetime

“…n w w = + q r for some q and r, and then considering the regime n  . We thus find a curvature-induced reduction in particle number, as noted in [33], and we recover equation for some q and r, the coefficient for which the curvature-dependent contribution is largest is b e e p = + --- (12), one can see that it is in principle possible to conduct an experiment for long enough that the curvature-dependent contribution dominates, since in the b mn for modes other than q and r (equation (11)), the value of T only serves to set the phases. Taking the massive body to be the Earth, and considering the parameters used in the SQUID setup of [27] at the surface, one finds that the observation of this resonance would take 10 17 times longer than observation of the usual parametric resonance, which is evidently impracticable.…”

“…The formal solution to equation (5) can be written using the time-ordered exponential. Consider motion between t = 0 and t = T, and following [33] let us define…”

“…The formal solution to equation ( 5) can be written using the time-ordered exponential. Consider motion between t = 0 and t = T , and following [33] let us define Θ(t) = ∫ t 0 dt ′ Ω(t ′ ). Now, since Ω is a diagonal matrix we can solve equation ( 5) in a manner analogous to the interaction picture of quantum mechanics, giving…”

“…Subsequent work has discussed the prospect that this negative energy flux is unphysical [31] or unobservable [32]. More recently, boundary motion in a static curved spacetime was investigated in [33], considering a cavity with a single mirror moving briefly over a short distance. However, a general description of the transformation of quantum field states due to the DCE in curved spacetime has remained an open problem.…”

Fifty Years of the Dynamical Casimir Effect

“…Various phenomena connected with the DCE were investigated in [482][483][484][485][486]. In particular, the DCE in curved spacetimes or in the presence of gravitational fields was studied in [487][488][489][490][491]. The role of the dynamical Casimir effect in the cosmological problems was studied in [158,492].…”