A Kerr Metric Solution in Tetrad Theory of Gravitation

TL;DR

This paper derives exact vacuum solutions in tetrad theory of gravitation, including the Schwarzschild and Kerr metrics, highlighting the role of axial symmetry and constants related to mass and angular momentum.

Contribution

It presents new exact solutions in tetrad gravity that reproduce known metrics and explores their properties, including singularities and physical constants.

Findings

Derived Schwarzschild and Kerr solutions within tetrad theory

Identified constants related to mass and angular momentum in the Kerr solution

Analyzed the singularity structure of the Kerr solution

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.