The geometry of the Ellis-Bronnikov wormhole is implemented in the Rastall and k-essence theories of gravity with a self-interacting scalar field. The form of the scalar field potential is determined in both cases. A stability analysis with respect to spherically symmetric time-dependent perturbations is carried out, and it shows that in k-essence theory the wormhole is unstable, like the original version of this geometry supported by a massless phantom scalar field in general relativity. In Rastall's theory, it turns out that a perturbative approach reveals the same inconsistency that was found previously for black hole solutions: time-dependent perturbations of the static configuration prove to be excluded by the equations of motion, and the wormhole is, in this sense, stable under spherical perturbations.
@article{arxiv.2102.10797,
title = {The simplest wormhole in Rastall and k-essence theories},
author = {Kirill A. Bronnikov and Vinícius A. G. Barcellos and Laura P. de Carvalh and Júlio C. Fabris},
journal= {arXiv preprint arXiv:2102.10797},
year = {2021}
}