Null second order corrections to Casimir energy in weak gravitational field

Abstract

The discussion of vacuum energy is currently a subject of great theoretical importance, specially concerning the cosmological constant problem in General Relativity. From Quantum Field Theory, it is stated that vacuum states subject to boundary conditions may generate tensions on these boundaries related to a measurable non-zero renormalized vacuum energy: the Casimir Effect. As such, investigating how these vacuum states and energy behave in curved backgrounds is just natural and might provide important results in the near future. In this paper we revisit a model of the Casimir Effect in weak gravitational field background, which has been proposed and further generalized in the literature. A trick originally used to simplify calculations is shown to lead to a wrong value for the energy shift, and by performing explicit mode expansion we arrive at an unexpected result: null gravitational correction even at order (M/R) 2 , in opposition to earlier results. 1

Null second order corrections to Casimir energy in weak gravitational field: the Schwinger's approach

“…The result obtained in the last section is in agreement with the ones from [45], however, as a remark regarding the mentioned work is made in [46] that could directly affect the result, we would like to address it here. The specific claim is that the mode solution presented in [45] does not satisfy proper orthonormalization conditions.…”

“…The result obtained in the last section is in agreement with the ones from [45], however, as a remark regarding the mentioned work is made in [46] that could directly affect the result, we would like to address it here. The specific claim is that the mode solution presented in [45] does not satisfy proper orthonormalization conditions. As no explicit demonstration is made, we would like to present ours, and reinforce the previous result, to which the method used in this paper shows agreement in a more general class of space-time metrics (14).…”

Casimir Wormholes in (2+1) Dimensions with Applications to the Graphene

“…It is worth also point out the contribution of the subject concerning the relationship between Casimir effect and traversable wormholes to the raise of new insights with respect to the issue if gravity in fact modifies the vacuum energy (and, vice-versa, if this latter gravitates), at least in weak field regime. This topic is actually object of discussion [9,10] and some proposals concerning observational investigations, as the Archimedes experiment [11].…”

Casimir effect in space-times of rotating wormholes

“…The more popular macroscopic physical manifestation of the vacuum fluctuations of quantum fields, the Casimir [25] effect, has been studied in several contexts [26][27][28][29][30]. It was originally related to the force that arises between two neutral, parallel, metallic and planar conductors placed in an ideal Minkowsky's vacuum.…”