Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes

TL;DR

This paper investigates how scalar fields condense around reflecting shells in Anti-de Sitter spacetimes, revealing discrete radii for hairy shells and bounds on their sizes, which enhances understanding of scalar field behaviors in curved backgrounds.

Contribution

It demonstrates scalar condensation around charged reflecting shells in AdS spacetime with both boundary conditions and establishes bounds on shell radii for condensation.

Findings

Scalar fields can condense around charged shells with both boundary conditions.

The radii of hairy shells are discrete, similar to flat spacetime cases.

Upper bounds exist for the radii of shells supporting scalar condensation.

Abstract

We study scalar condensations around asymptotically Anti-de Sitter(AdS) regular reflecting shells. We show that the charged scalar field can condense around charged reflecting shells with both Dirichlet and Neumann boundary conditions. In particular, the radii of the asymptotically AdS hairy shells are discrete, which is similar to cases in asymptotically flat spacetimes. We also provide upper bounds for the radii of the hairy Dirichlet reflecting shells and above the bound, the scalar field cannot condense around the shell.