The simplest wormhole in Rastall and k-essence 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.

15 pages, no figures

References in corpus (2)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis

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