https://doi.org/10.1140/epjp/s13360-023-04529-6
Regular Article
AdS waves in Brans-Dicke theory
1
Department of Physics, Faculty of Science, Istanbul University, Vezneciler, 34134, Istanbul, Turkey
2
Department of Physics, Faculty of Science, Marmara University, Kadikoy, 34722, Istanbul, Turkey
Received:
21
June
2023
Accepted:
26
September
2023
Published online:
9
October
2023
In this paper, we investigate Anti-de Sitter (AdS) wave solutions, also known as Siklos solutions, for the Brans-Dicke theory with an arbitrary potential in the Jordan frame. The form of the scalar field and potential supporting an AdS wave can be obtained from the well-known work presented by Ayón-Beato et. al. for Einstein-Scalar theory with a nonminimally coupled scalar field or simply by explicitly solving JBD field equations. The dependence of the scalar field on the particular coordinate is crucial in the Jordan frame, and there is no solution where scalar field is only depending on the retarded null coordinate, which is conflicting with Brinkman pp-wave solutions where this is possible and also with Siklos solution in Einstein frame BD theory where the solution is only possible if the scalar field depends only on the retarded null coordinate and the potential is constant. In order to find various vacuum, null fluid, or electromagnetic field solutions, the only remaining metric field equation is integrated and analogues of known solutions of GR are obtained such as Kaigorodov vacuum solution, generalized Defrise solutions and Oszvath electromagnetic field solutions. We also determine the configurations where stealth AdS waves can be obtained in this setting in a vacuum or null fluid background.
Hatice Özer and Özgür Delice have contributed equally to this work.
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