Line Sources in Brans-Dicke Theory of Gravity

We investigate how the gravitational field generated by line sources can be characterized in Brans-Dicke theory of gravity. Adapting an approach previously developed by Israel who solved the same problem in general relativity we show that in Brans-Dicke theory's case it is possible to work out the field equations which relate the energy-momentum tensor of the source to the scalar field, the coupling constant $\omega$ and the extrinsic curvature of a tube of constant geodesic radius centered on the line in the limit when the radius shrinks to zero. In this new scenario two examples are considered and an account of the Gundlach and Ortiz solution is included. Finally, a brief discussion of how to treat thin shells in Brans-Dicke theory is given.Comment: 21 pages, RevTex; added a discussion on the Gundlach and Ortiz solutio

Is the proton radius puzzle evidence of extra dimensions?

The proton charge radius inferred from muonic hydrogen spectroscopy is not compatible with the previous value given by CODATA-2010, which, on its turn, essentially relies on measurements of the electron-proton interaction. The proton's new size was extracted from the 2S-2P Lamb shift in the muonic hydrogen, which showed an energy excess of 0.3 meV in comparison to the theoretical prediction, evaluated with the CODATA radius. Higher-dimensional gravity is a candidate to explain this discrepancy, since the muon-proton gravitational interaction is stronger than the electron-proton interaction and, in the context of braneworld models, the gravitational potential can be hugely amplified in short distances when compared to the Newtonian potential. Motivated by these ideas, we study a muonic hydrogen confined in a thick brane. We show that the muon-proton gravitational interaction modified by extra dimensions can provide the additional separation of 0.3 meV between 2S and 2P states. In this scenario, the gravitational energy depends on the higher-dimensional Planck mass and indirectly on the brane thickness. Studying the behavior of the gravitational energy with respect to the brane thickness in a realistic range, we find constraints for the fundamental Planck mass that solve the proton radius puzzle and are consistent with previous experimental bounds.Comment: Updated with new dat