A Kerr Metric Solution in New General Relativity

TLDR: In this paper, an exact solution of the vacuum gravitational field equation in new general relativity was given, which gives the Kerr metric and the parallel vector fields are axially symmetric.

Abstract: We give an exact solution of the vacuum gravitational field equation in new general relativity. The solution gives the Kerr metric and the parallel vector fields are axially symmetric. A parameter h in the expression of the metric is related to the angular momentum of the rotating source, when the spin density S,f of the gravitational source satisfies the condition a~Si/=O. In the Kerr metric space· time, we cannot discriminate new general relativity from general relativity, so far as scalar, the Dirac and the Yang-Mills fields and macroscopic bodies ·are used as probes. The space-time given by the solution does not have singularities at all, although it has an "effective singularity". Two kinds of Schwarzschild metric solutions, one is our solution with h=O and the other is a solution given by Hayashi and Shirafuji, are physically equivalent with each other. Nevertheless, these are markedly different from each other with regard to the asymptotic behavior of the torsion tensor for r-->OO and the space-time singularities.