Casimir effect in the Fulling-Rindler vacuum

Abstract

The vacuum expectation values of the energy-momentum tensor are investigated for massless scalar fields satisfying Dicichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on two infinite parallel plates moving by uniform proper acceleration through the Fulling-Rindler vacuum. The scalar case is considered for general values of the curvature coupling parameter and in an arbitrary number of spacetime dimension. The mode-summation method is used with combination of a variant of the generalized Abel-Plana formula. This allows to extract manifestly the contributions to the expectation values due to a single boundary. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction terms. The first one contains well known surface divergences and needs a further regularization. The interaction forces between the plates are always attractive for both scalar and electromagnetic cases. An application to the 'Rindler wall' is discussed.

Casimir energy in the Fulling-Rindler vacuum

“…From these expressions it follows that the coefficients u l (t) have the structure 17) with the numerical coefficients u lm . From the recurrence relations for the polynomials u l (t) (see [33]), the following recurrence formulae can be obtained for the coefficients u lm : 18) where m = 0, 1, .…”

“…As a result the eigenmodes are independent of the curvature coupling parameter and, hence, the Casimir energy will not depend on this parameter. However, the local characteristics of the vacuum such as energy density and vacuum stresses depend on the parameter ζ [16,17].…”

“…[17], the vacuum forces acting on the boundaries can be presented as a sum of the self-action and interaction forces. It can be easily checked that the interaction forces are related to the energy (3.11) by the standard thermodynamical relations…”

“…The vacuum expectation values of the energy-momentum tensors for scalar and electromagnetic fields for the geometry of two parallel plates moving by uniform acceleration are investigated in Ref. [17]. In particular, the vacuum forces acting on the boundaries are evaluated.…”

“…In Refs. [16,17] the mode summation method is used in combination with the generalized Abel-Plana summation formula [18]. This allowed us to present the vacuum expectation values in the terms of the purely Rindler and boundary parts.…”