Abstract
In this paper we consider the dynamics of a massive spinor field in the background of the acoustic black hole spacetime. Although this effective metric is acoustic and describes the propagation of sound waves, it can be considered as a toy model for the gravitational black hole. In this manner, we study the properties of the dynamics of the fermion field in this “gravitational” rotating black hole as well as the vortex background. We compute the differential cross section through the use of the partial wave approach and show that an effect similar to the gravitational Aharonov–Bohm effect occurs for the massive fermion field moving in this effective metric. We discuss the limiting cases and compare the results with the massless scalar field case.
Highlights
In 1959, Aharonov and Bohm showed that when the wave function of a charged particle passing around a region with the magnetic flux, despite the magnetic field being negligible in the region through which the particle passes, experiences a phase shift as a result of the enclosed magnetic field [43]
The effective sonic black hole spacetime is not the one fermion fields would observe, but it can be used as a toy model and a mathematical tool to study and as a result understand better the dynamics of the massive and massless fermion fields in a gravitational rotating black hole as well as a vortex background and shed light on the underlying physics
We have studied the differential cross section of a massive spinor field in the background of the acoustic black hole spacetime, as a toy model for the gravitational rotating black hole, using the partial wave approach
Summary
In 1959, Aharonov and Bohm showed that when the wave function of a charged particle passing around a region with the magnetic flux, despite the magnetic field being negligible in the region through which the particle passes, experiences a phase shift as a result of the enclosed magnetic field [43]. An interesting system was investigated in [64], where it was shown that planar waves scattered by a draining bathtub vortex develops a modified AB effect that has a dependence on two dimensionless parameters, related to the circulation and draining rates [65]. The effective sonic black hole spacetime is not the one fermion fields would observe, but it can be used as a toy model and a mathematical tool to study and as a result understand better the dynamics of the massive and massless fermion fields in a gravitational rotating black hole as well as a vortex background and shed light on the underlying physics. In the present study we consider the dynamics of a massive Dirac spinor field in a curved spacetime and apply the acoustic black hole metric to obtain the differential cross section for scattered planar waves which leads to an analog AB effect.
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