On the instability of charged wormholes supported by a ghost scalar field

TL;DR

This paper investigates the stability of charged wormholes supported by a ghost scalar field, revealing that most solutions are linearly unstable, with some cases exhibiting exponential growth of perturbations, indicating inherent instability.

Contribution

The study extends previous uncharged wormhole stability analysis to charged cases, deriving a four-parameter family of solutions and analyzing their linear stability.

Findings

All subcritical and critical solutions are linearly unstable.

Numerical evidence suggests supercritical solutions also have unstable modes.

Charged wormholes generally exhibit exponential growth of perturbations.

Abstract

In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einstein's field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable with respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black hole or undergo a rapid expansion. Here, we consider charged generalization of the previous models by adding to the gravitational and ghost scalar field an electromagnetic one. We first derive the most general static, spherically symmetric wormholes in this theory and show that they give rise to a four-parameter family of solutions. This family can be naturally divided into subcritical, critical and supercritical solutions depending on the sign of the sum of the asymptotic masses. Then, we analyze the linear stability of these solutions. We prove that all subcritical and all critical solutions possess one exponentially in time growing mode. It follows that all subcritical and critical wormholes are linearly unstable. In the supercritical case we provide numerical evidence for the existence of a similar unstable mode.