In this paper we consider the Dirac equation in curved spacetime which has a line element given by
with electromagnetic field
. We calculate the spinorial wave function and the energy spectrum of the Dirac oscillator in the curved spacetime, and from this result, we are able to return the solution in the flat spacetime. We consider two forms of symmetry in the coupling of the spin 1/2 particle with the electromagnetic field and curved spacetime: exact spin symmetry V(r) = U(r) and pseudo-spin symmetry
.
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