https://doi.org/10.1140/epjc/s10052-024-13420-2
Regular Article - Theoretical Physics
On the stability of electrovacuum space-times in scalar–tensor gravity
1
Center of Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, 119361, Moscow, Russia
2
Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia
3
National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, 115409, Moscow, Russia
4
Department of Theoretical Physics and Computer Science, Samarkand State University, 140104, Samarkand, Uzbekistan
5
Karshi State University, Kochabog Street, 180103, Karshi City, Uzbekistan
Received:
24
August
2024
Accepted:
25
September
2024
Published online:
8
October
2024
We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter 
. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
