A Kerr Metric Solution in Tetrad Theory of Gravitation

Abstract

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.