A new theory of tensor-scalar gravity coupled to Aharonov-Bohm electrodynamics

TL;DR

This work develops a tensor–scalar theory of gravity that extends Brans–Dicke gravity by including an additional scalar $ψ$ and coupling to Aharonov–Bohm electrodynamics through a source $J$ that depends on the AB scalar $S=∇_μ A^μ$. In the weak-field limit, the authors derive coupled linearized equations for the metric perturbation, the scalars $φ$ and $ψ$, and the AB sector, showing how $S^2$-type sources feed back into the gravitational potentials via derivatives of the AB couplings. They analyze 1-D traveling and soliton-like solutions for $S$, and study resonant cavities where time-averaged forces arise from nonconserved currents, deriving order-of-magnitude estimates that depend on the unknown VEVs $ψ_0$ and the nonconservation parameter $γ$. The results provide a framework to model gravity–macroscopic quantum interactions and indicate that, while potentially detectable under extreme conditions, current experimental constraints place stringent limits on the magnitude of these effects and leave open substantial uncertainty about practical observability.

Abstract

Tensor-scalar theories of gravitation are commonly employed as extensions of General Relativity that allow to describe a much wider phenomenology. They are also naturally generated as low energy limit of higher-dimensional or unified theories, and the gravitational scalar components can represent quantum corrections to the Einstein theory. The coupling of the scalars to an e.m. field does not introduce any relevant new physics if the e.m. action has the usual Maxwell form, implying a vanishing trace of the e.m. energy-momentum tensor. In the case of the extended Aharonov-Bohm electrodynamics some interesting new situations are possible, which in this work are analyzed in the gravitational weak-field approximation and for a basic version of tensor-scalar gravity involving only a Brans-Dicke field plus another scalar. Since the Aharonov-Bohm theory differs from Maxwell theory only in the presence of anomalous sources with local violation of charge conservation, which is thought to be possible only at a quantum level, the resulting formal framework can be useful to model interactions between gravitation and physical systems with macroscopic quantization. The theory contains some unknown parameters, the most important being the VEV $ψ_0$ of the second gravitational scalar and the level $γ$ of violation of local charge conservation in the e.m. sector. An attempt is done to relate these parameters to some experimental constraints. However, there is presently much space left for uncertainty.