Electrically charged and neutral wormhole instability in scalar-tensor gravity

TL;DR

This paper investigates the stability of scalar-tensor wormholes with or without electric charge, demonstrating their instability under symmetric perturbations through analytical and numerical methods.

Contribution

It provides a comprehensive stability analysis of scalar-tensor wormholes, including charged and neutral cases, using both analytical proofs and numerical validation.

Findings

Wormholes with zero or small electric charge are unstable.

Stability analysis employs self-adjoint operator theory.

Numerical computations confirm analytical results.

Abstract

We study the stability of static, spherically symmetric, traversable wormholes with or without an electric charge, existing due to conformal continuations in a class of scalar-tensor theories with zero scalar field potential (so that Penney's or Fisher's well-known solutions hold in the Einstein conformal frame). Specific examples of such wormholes are those with nonminimally (e.g., conformally) coupled scalar fields. All boundary conditions for scalar and metric perturbations are taken into account. All such wormholes with zero or small electric charge are shown to be unstable under spherically symmetric perturbations. The instability is proved analytically with the aid of the theory of self-adjoint operators in Hilbert space and is confirmed by numerical computations.