Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis

TL;DR

This paper proves that all static, spherically symmetric wormholes supported by a ghost scalar field are linearly unstable, with a single exponential growth mode, and characterizes the timescale of this instability.

Contribution

It provides a rigorous linear stability analysis of ghost scalar field wormholes, showing their inherent instability and identifying the growth mode and timescale.

Findings

All solutions are linearly unstable.

Each solution has exactly one unstable mode.

The instability timescale is roughly the throat radius divided by the speed of light.

Abstract

We examine the linear stability of static, spherically symmetric wormhole solutions of Einstein's field equations coupled to a massless ghost scalar field. These solutions are parametrized by the areal radius of their throat and the product of the masses at their asymptotically flat ends. We prove that all these solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. The associated time scale is shown to be of the order of the wormhole throat divided by the speed of light. The nonlinear evolution is analyzed in a subsequent article.