Casimir-Polder potential for a metallic cylinder in cosmic string spacetime

TL;DR

This paper analyzes the Casimir-Polder potential for a polarizable particle near a metallic cylinder in cosmic string spacetime, deriving general expressions and examining the force's behavior in different regions.

Contribution

It provides the first detailed derivation of the Casimir-Polder potential in a cosmic string background with a metallic cylindrical shell, including anisotropic polarizability effects.

Findings

Shell-induced potential dominates near the shell.

Pure string potential dominates near the string and at large distances.

For isotropic polarizability, the force is repulsive in the interior and exterior regions.

Abstract

Casimir-Polder potential is investigated for a polarizable microparticle in the geometry of a straight cosmic string with a metallic cylindrical shell. The electromagnetic field Green tensor is evaluated on the imaginary frequency axis. The expressions for the Casimir-Polder potential is derived in the general case of anisotropic polarizability for the both interior and exterior regions of the shell. The potential is decomposed into pure string and shell-induced parts. The latter dominates for points near the shell, whereas the pure string part is dominant near the string and at large distances from the shell. For the isotropic case and in the region inside the shell the both pure string and shell-induced parts in the Casimir-Polder force are repulsive with respect to the string. In the exterior region the shell-induced part of the force is directed toward the cylinder whereas the pure string part remains repulsive with respect to the string. At large distances from the shell the total force is repulsive.