Abstract
A quantum particle is considered in the background gravitational field due to a tubular matter source with axial interior magnetic field and vanishing exterior magnetic field. It is shown that in the locally flat spacetime around this tubular matter source, the wavefunction, the energy spectrum and the probability current depend on the amount of matter and magnetic field. These dependences represent gravitational analogues of the Aharonov-Bohm effect in electrodynamics.
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