The simplest wormhole in Rastall and k-essence theories

TL;DR

This paper explores the geometry and stability of Ellis-Bronnikov wormholes within Rastall and k-essence gravity theories, revealing instability in k-essence and stability in Rastall under spherical perturbations.

Contribution

It determines the scalar field potentials and analyzes the stability of wormholes in both theories, highlighting differences from general relativity.

Findings

K-essence wormhole is unstable under spherical perturbations.

Rastall wormhole remains stable against spherical perturbations.

Scalar field potentials are explicitly derived for both theories.

Abstract

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.