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

TL;DR

This paper explores a scalar-tensor gravity extension coupled with Aharonov-Bohm electrodynamics, analyzing its effects on superconductors and predicting conditions for observable anomalous gravitational signals.

Contribution

It introduces a novel scalar-tensor framework with dynamical scalar modes affecting superconductors, providing new theoretical insights and scaling relations for experimental detection.

Findings

Scalar mode $S$ induces significant electro-gravitational coupling in superconductors.

A saturation solution for $S$ is identified, leading to threshold conditions for macroscopic effects.

Scaling relations for gravitational signals are derived, matching experimental thresholds.

Abstract

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.