Scalar-tensor gravity and Aharonov-Bohm electrodynamics with bosons: applications to superconductors

We study a scalar-tensor extension of gravity with two scalar fields coupled to the Aharonov-Bohm extension of electrodynamics, where the scalar mode $S\equiv\partial_\mu A^\mu$ is dynamical. In this framework the trace of the electromagnetic energy-momentum tensor is nonvanishing and the scalar $S$ induces an electro-gravitational coupling that can be enhanced by the vacuum expectation value of the second gravitational scalar. For bosonic matter described by a macroscopic wavefunction (as in superconductors), the coupling to the electromagnetic potential generates $S$ already at the semiclassical level, implying sizable junction-induced discontinuities. Including the scalar-tensor sector yields a nonlinear system for $S$ and a gravitational scalar combination $\beta$ that admits a bulk saturation solution $S_{\rm sat}^2=(\Lambda\lambda_L^2)^{-1}$ and a corresponding threshold condition for macroscopic effects. We apply these results to pulsed discharges across normal-superconducting junctions and obtain scaling relations for the onset of anomalous gravitational signals in terms of current density, pulse duration, and superconducting volume, consistent with reported threshold behavior in two independent experimental configurations for a single microscopic parameter. We also present time-dependent propagating solutions in the weak-field regime and derive a class of one-dimensional traveling exact solutions of the nonlinear vacuum Einstein equations.