On the interaction of the Dirac oscillator with the Aharonov–Casher system in topological defect backgrounds

• Influence of the Aharonov–Casher effect on the Dirac oscillator.
• Exact solutions of the Dirac equation in topological defect spacetimes.
• Dependence of the relativistic energy levels on the Aharonov–Casher geometric phase.
• Influence of curvature and torsion on the relativistic energy levels and the Dirac spinors.

In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.