We calculate the finite vacuum energy density of the scalar and electromagnetic fields inside a Casimir apparatus made up of two conducting parallel plates in a general weak gravitational field. The metric of the weak gravitational field has a small deviation from flat spacetime inside the apparatus, and we find it by expanding the metric in terms of small parameters of the weak background. We show that the metric found can be transformed via a gauge transformation to the Fermi metric. We solve the Klein-Gordon equation exactly and find mode frequencies in Fermi spacetime. Using the fact that the electromagnetic field can be represented by two scalar fields in the Fermi spacetime, we find general formulas for the energy density and mode frequencies of the electromagnetic field. Some well-known weak backgrounds are examined and consistency of the results with the literature is shown.

In 1+3 (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea one could examine the response of vacuum energy to the presence of a stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. The results are given explicitly for a Casimir apparatus in the weak field limit of a Kerr hole.Comment: 10 pages, RevTex, more typos corrected (combined with arXiv:1003.0614 published in PRD

In a recent paper [1] using a conjecture it is shown how one can calculate the effect of a weak stationary gravitational field on vacuum energy in the context of Casimir effect in an external gravitational field treated in 1 + 3 formulation of spacetime decomposition.. In this article, employing quantum field theory in curved spacetime, we explicitly calculate the effect of a weak static gravitational field on virtual massless scalar particles in a Casimir apparatus. It is shown that, as expected from the proposed conjecture, both the frequency and renormalized energy of the virtual scalar field are affected by the gravitational field through its index of refraction. This could be taken as a strong evidence in favour of the proposed conjecture. Generalizations to weak stationary spacetimes and virtual photons are also discussed. * Electronic address: bornadel@khayam.ut.ac.ir † Electronic address: nouri@theory.ipm.ac.ir, corresponding author 1

The energy of the massless scalar field inside parallel Casimir plates in a general weak gravitational field under the influence of Robin boundary conditions is calculated. The mode frequencies are found in asymptotic limits and consistency of results with the literature is shown. Experimental evidence for detection of corrections is explored. Finding Mode Frequencies Inside the Plates for Robin Boundary ConditionsThe problem is to find mode frequencies of a scalar Klein-Gordon field inside an apparatus consisting of two conducting parallel plates in a general weak gravitational field under the influence of the Robin boundary conditions. The spacetime is dsecribed by the common spherical r, θ, φ coordinates. The plates are in a

Influence of gravity on the quantum vacuum of a massless minimally coupled scalar field under Robin boundary conditions on parallel plates is investigated. We introduce the detailed calculation of the volume energy for the case the gravitational background is weak in its most general form for a static spacetime. It founds that the quantum vacuum usually reacts to the gravitational field by decreasing the Casimir energy. In addition, we find sufficient conditions under which the Casimir force increases. Interestingly, the first order perturbation corrections, are present in the obtained formula for the volume energy. We show that for some specific choices of parameters, the energy is independent of Robin coefficients. Consistency with the literature is shown in some limiting cases and well-known examples are presented for both an increase or decrease in the volume energy.