Quasi-Normal Modes of a Natural AdS Wormhole in Einstein-Born-Infeld Gravity

TL;DR

This paper investigates the stability of a novel AdS wormhole in Einstein-Born-Infeld gravity by analyzing scalar field quasi-normal modes, revealing stability conditions related to a BF-like bound and parameter dependencies.

Contribution

It introduces a new natural AdS wormhole solution in Einstein-Born-Infeld gravity and analyzes its perturbation stability, including the effects of parameters on quasi-normal modes.

Findings

Perturbations are stable when scalar mass exceeds a BF-like bound in the GR limit.

The BF-like bound shifts with cosmological constant and angular momentum.

Unstable modes can be oscillatory or non-oscillatory, depending on mode parameters.

Abstract

We study the matter perturbations of a new AdS wormhole in (3+1)-dimensional Einstein-Born-Infeld gravity, called "natural wormhole", which does not require exotic matters. We discuss the stability of the perturbations by numerically computing the quasi-normal modes (QNMs) of a massive scalar field in the wormhole background. We investigate the dependence of quasi-normal frequencies on the mass of scalar field as well as other parameters of the wormhole. It is found that the perturbations are always stable for the wormhole geometry which has the general relativity (GR) limit when the scalar field mass m satisfies a certain, tachyonic mass bound m^2 > m^2_* with m^2_* < 0, analogous to the Breitenlohner-Freedman (BF) bound in the global-AdS space, m^2_BF = 3 Lambda/4. It is also found that the BF-like bound m^2_* shifts by the changes of the cosmological constant Lambda or angular-momentum number l, with a level crossing between the lowest complex and pure-imaginary modes for zero angular momentum l = 0. Furthermore, it is found that the unstable modes can also have oscillatory parts as well as non-oscillatory parts depending on whether the real and imaginary parts of frequencies are dependent on each other or not, contrary to arguments in the literature. For wormhole geometries which do not have the GR limit, the BF-like bound does not occur and the perturbations are stable for arbitrary tachyonic and non-tachyonic masses, up to a critical mass m^2_c > 0 where the perturbations are completely frozen.