Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons

TL;DR

This paper analyzes how Robin boundary conditions and extra dimensions influence the Casimir effect, revealing conditions for attraction, repulsion, and stable equilibrium points, with implications for braneworld models and piston geometries.

Contribution

It provides a comprehensive evaluation of the Casimir energy and force with general Robin boundary conditions in higher-dimensional spacetimes, including stability analysis and applications to braneworld scenarios.

Findings

Casimir force can be attractive or repulsive depending on boundary conditions and Robin coefficients.

Existence of a stable equilibrium point for the interplate distance due to Casimir forces.

Extra dimensions enhance the stability of the equilibrium point.

Abstract

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a $(D+1)$-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.