On the stability of exceptional Brans-Dicke wormholes

TL;DR

This paper investigates the stability of specific Brans-Dicke wormholes with zero coupling constant, finding that charged wormholes are stable under radial perturbations, while neutral ones are unstable.

Contribution

It extends previous stability analyses to exceptional Brans-Dicke solutions with $$, revealing stability conditions based on charge presence.

Findings

Charged wormholes are stable under radial perturbations.

Neutral wormholes are unstable in the symmetric case.

Stability depends on the charge parameter q.

Abstract

In our previous papers we have analyzed the stability of vacuum and electrovacuum static, spherically symmetric space-times in the framework of the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories (STT) of gravity. In the present paper, we continue this study by examining the stability of exceptional solutions of the Brans-Dicke theory with the coupling constant $\omega =0$ that were not covered in the previous studies. Such solutions describe neutral or charged wormholes and involve a conformal continuation: the standard conformal transformation maps the whole Einstein-frame manifold ${\mathbb M}_E$ to only a part of the Jordan-frame manifold ${\mathbb M}_J$, which has to be continued beyond the emerging regular boundary S, and the new region maps to another manifold ${\mathbb M}_{E-}$. The metric in ${\mathbb M}_J$ is symmetric with respect to S only if the charge $q$ is zero. Our stability study concerns radial (monopole) perturbations, and it is shown that the wormhole is stable if $q \ne 0$ and unstable only in the symmetric case $q=0$