  Using an axial parallel vector field we obtain two exact solutions of a
vacuum gravitational field equations. One of the exact solutions gives the
Schwarzschild metric while the other gives the Kerr metric. The parallel vector
field of the Kerr solution have an axial symmetry. The exact solution of the
Kerr metric contains two constants of integration, one being the gravitational
mass of the source and the other constant $h$ is related to the angular
momentum of the rotating source, when the spin density ${S_{i j}}^\mu$ of the
gravitational source satisfies $\partial_\mu {S_{i j}}^\mu=0$. The singularity
of the Kerr solution is studied.
