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

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