https://doi.org/10.1140/epjp/s13360-025-06605-5
Regular Article
Gravitational dipole moment in braneworld model
1
Unidade Acadêmica de Engenharia de Produção, Universidade Federal de Campina Grande, Caixa Postal 10071, 58540-000, Sumé, Paraíba, Brazil
2
Unidade Acadêmica de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58429-900, Campina Grande, Paraíba, Brazil
3
Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Caixa Postal 58429-970, Campina Grande, Paraíba, Brazil
a
eugenio.maciel@df.ufcg.edu.br
Received:
22
January
2025
Accepted:
30
June
2025
Published online:
19
July
2025
We investigate the gravitational effects on the relativistic Dirac theory of a system such as a Hydrogen atom in the braneworld scenario. A gravitational dipole moment like contribution arises in the non-relativistic Hamiltonian of the system through an exact Foldy–Wouthuysen transformation. This term violates the equivalence principle for the weak interaction that is restored in the average over the spins. Furthermore, it feels the effects of the extra dimensions, so that in a Universe with two additional spatial dimensions its energy contribution is amplified by an order of concerning to the energy of this term for ordinary space. The compactification radius for a Universe with two extra dimensions is within the experimental limits, where deviations from the inverse square law are being tested. This suggests that the energy value for the gravitational dipole term in this scenario may lead us to search for traces of extra dimensions in atomic spectroscopy, as well as experimental constraints for these dimensions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.