Casimir repulsion between metallic objects in vacuum

TL;DR

This paper demonstrates a specific metallic geometry in vacuum where Casimir forces become repulsive, confirmed through symmetry arguments and numerical calculations, though it does not support stable levitation.

Contribution

It provides the first example of Casimir repulsion in a simple metallic geometry and verifies it with numerical methods for both ideal and realistic metals.

Findings

Casimir repulsion occurs in the proposed geometry

Numerical confirmation for perfect and realistic metals

Particle is unstable to displacements, preventing stable levitation

Abstract

We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.