Normal modes of charged AdS solitons

TL;DR

This paper investigates the stability of charged AdS solitons by analyzing scalar field perturbations, revealing stable normal modes and scaling laws that support the positive energy conjecture in such spacetimes.

Contribution

It provides a detailed numerical analysis of normal modes in charged AdS solitons, establishing their stability and uncovering scaling behaviors.

Findings

Normal mode frequencies are real, indicating stability.

Scaling laws and asymptotic behaviors of spectra are identified.

Supports the positive energy conjecture in AdS spacetimes.

Abstract

We study massive charged scalar field perturbations in four- and five- dimensional charged anti-de Sitter soliton spacetimes. Appropriate boundary conditions are established via a local analysis of the perturbation equations. The normal mode spectra are then calculated numerically using the Horowitz-Hubeny method and a collocation method. We reveal scaling laws and asymptotic behaviors governing the normal mode spectra. The reality of the normal mode frequencies indicates the dynamic stability of the soliton, which in turn provides support for the positive energy conjecture in asymptotically locally anti-de Sitter spacetime.