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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24787 |
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Table of Contents:
- We examine whether rotating frames and stationary gravitomagnetic backgrounds can provide a meaningful link to extended Aharonov-Bohm electrodynamics without invoking microscopic charge non-conservation. For standard generally covariant, locally $U(1)$-invariant matter, the answer at the microscopic level is negative: the physical four-current remains covariantly conserved, so neither rotation nor stationary gravitomagnetism by themselves generate a genuine source for the scalar sector. A weaker but still useful connection nevertheless emerges after a $3+1$ decomposition with respect to a rotating observer congruence. In that description, the observer-measured transport current on the spatial slice obeys a projected continuity equation containing an exact split source term $I_{\mathrm{split}} \equiv \frac{1}{N} D_i(ρ\,β^i)$, which reduces in the weak-field regime to $I_G = D_i(ρ\,β^i)$. This term is not a frame-independent microscopic anomaly; it is the bookkeeping term that appears when covariant conservation is rewritten in transport variables adapted to a rotating slicing. We then propose a phenomenological AB-type closure in which this split source drives the scalar sector on finite-scale rotating systems. In the rigid-rotation weak-field limit, the source reduces to $I_G = (\boldsymbolΩ \times \mathbf{r})\cdot \nabla ρ$, and for localized transients to $ I_G = Ω\partial_ϕ(δρ_s)$. The resulting framework is therefore effective rather than fundamental, observer-tied rather than local-inertial, and experimentally meaningful only at mesoscopic or macroscopic scales. It yields concrete operational signatures, including reversal under $Ω\to -Ω$, suppression for nearly axisymmetric charge distributions, and sensitivity to transient non-axisymmetric charge structure.