Instability Analysis of Massive Static Phantom Wormholes via the Spectral Method

TL;DR

This study uses spectral methods to analyze the stability of massive static phantom wormholes, revealing new purely imaginary quasinormal modes and stability thresholds related to the wormhole's size and perturbation type.

Contribution

It introduces the detection of purely imaginary QNMs and clarifies stability conditions for phantom wormholes based on spectral analysis.

Findings

Purely imaginary QNMs were identified, not seen in previous studies.

Instability occurs when the ratio of Schwarzschild radius to wormhole throat exceeds 1.0.

Wormholes are stable when the throat size is much larger than the Schwarzschild radius.

Abstract

Using the spectral method, we investigate the scalar and axial quasinormal modes (QNMs) of massive static phantom wormholes. Our results reveal the existence of purely imaginary QNMs that were not identified in previous studies, suggesting potential (in)stabilities as the ratio of the Schwarzschild radius to the wormhole throat varies within a specific range. For scalar perturbations, instabilities arise when this ratio exceeds $1.0$, with the threshold value of $1.0$ itself included. In the case of axial perturbations, the onset of instability occurs at smaller ratios, reflecting the impact of gravitational waves on the wormhole's stability. The findings suggest that the wormhole remains stable when the throat size significantly exceeds the Schwarzschild radius. Our results align with existing literature but offer new insights into the stability conditions of phantom wormholes.