Eur. Phys. J. C (2017) 77: 239
https://doi.org/10.1140/epjc/s10052-017-4801-1

Regular Article - Theoretical Physics

Aharonov–Bohm effect for a fermion field in a planar black hole “spacetime”

¹ Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, Campina Grande, Paraíba, 58429-900, Brazil
² Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba, 58051-970, Brazil
³ Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 21945, Rio de Janeiro, Brazil

^* e-mail: a.mohammadi@fisica.ufpb.br

Received: 7 March 2017
Accepted: 31 March 2017
Published online: 12 April 2017

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.