Stability of asymptotically AdS wormholes in vacuum against scalar field perturbations

TL;DR

This paper investigates the stability of asymptotically AdS wormholes in vacuum against scalar field perturbations, deriving exact spectra and stability bounds that depend on the scalar mass, coupling, and base manifold geometry.

Contribution

It provides analytical expressions for the scalar field spectrum and stability conditions for various perturbations in asymptotically AdS wormholes, including nonminimal coupling and different fall-off behaviors.

Findings

Stability is guaranteed if the scalar mass squared is above a negative bound.

Exact spectral formulas are derived for different scalar field couplings.

Stability ranges depend on the base manifold and fall-off conditions.

Abstract

The stability of certain class of asymptotically AdS wormholes in vacuum against scalar field perturbations is analyzed. For a free massive scalar field, the stability of the perturbation is guaranteed provided the squared mass is bounded from below by a negative quantity. Depending on the base manifold of the AdS asymptotics, this lower bound could be more stringent than the Breitenlohner-Freedman bound. An exact expression for the spectrum is found analytically. For a scalar field perturbation with a nonminimal coupling, slow fall-off asymptotic behavior is also allowed, provided the squared mass fulfills certain negative upper bound. Although the Ricci scalar is not constant, an exact expression for the spectrum of the scalar field can also be found, and three different quantizations for the scalar field can be carried out. They are characterized by the fall-off of the scalar field, which can be fast or slow with respect to each asymptotic region. For these perturbations, stability can be achieved in a range of negative squared masses which depends on the base manifold of the AdS asymptotics. This analysis also extends to a class of gravitational solitons with a single conformal boundary.