Electromagnetic Casimir piston in higher dimensional spacetimes

Abstract

We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the $(4+n)$-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the 4-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the 4-dimensional Minkowski spacetime if $h$ is nonzero.

22 pages, 4 figures

References in corpus (23)

• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Casimir piston for massless scalar fields in three dimensions
• Casimir Forces in a Piston Geometry at Zero and Finite Temperatures
• Kaluza-Klein models as pistons
• The Casimir Force in Randall Sundrum Models
• Casimir force for a scalar field in warped brane worlds
• The Casimir Force in Randall Sundrum Models with q+1 dimensions
• The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
• The Casimir force on a piston in the spacetime with extra compactified dimensions
• Casimir Effect confronts Cosmological Constant
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
• Finite temperature Casimir effect in piston geometry and its classical limit
• The Casimir Effect for Conical Pistons
• 3D scalar model as a 4D perfect conductor limit: dimensional reduction and variational boundary conditions
• Casimir effect for curved boundaries in Robertson-Walker spacetime
• What measurable zero point fluctuations can(not) tell us about dark energy
• On Taming the Warped Radion with Supersymmetry