Gravitational Dipole Moment in Braneworld Model

TL;DR

This paper explores how extra dimensions in braneworld models influence gravitational effects on atomic systems, revealing a gravitational dipole moment that could help detect extra dimensions through atomic spectroscopy.

Contribution

It introduces a gravitational dipole moment in the nonrelativistic Hamiltonian of atomic systems within braneworld scenarios, linking extra dimensions to observable atomic effects.

Findings

Gravitational dipole moment arises in the nonrelativistic limit.

Energy contribution is amplified by extra dimensions, up to 10^{16} eV.

Potential for atomic spectroscopy to detect extra dimensions.

Abstract

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 nonrelativistic 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 $\sim 10^{16}\ \text{eV}$ 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.