Regular Article - Theoretical Physics
The simplest wormhole in Rastall and k-essence theories
Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, 119361, Moscow, Russia
2 Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia RUDN University, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia
3 National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, 115409, Moscow, Russia
4 Núcleo Cosmo-ufes and Departamento de Fíísica, CCE, Universidade Federal do Espírito Santo, Vitória, CEP 29075-910, ES, Brazil
Accepted: 18 April 2021
Published online: 6 May 2021
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.
© The Author(s) 2021
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