  In this paper we study the Dirac field theory interacting with external
gravitation field, described with tetrad of the form
$e_b^\mu(x)=\varepsilon(\delta_b^\mu+\omega_{ba}^\mu x^a)$, where
$\varepsilon=1$ for $\mu=0$ and $\varepsilon=i$ for $\mu=1,2,3.$ The
probability density of the vacuum-vacuum pair creation is given. In particular
case of vanishing electromagnetic fields, we point out how this deformation
modify the amplitude transition. The corresponding Dirac equation is solved.
