A Charged Kerr Metric Solution in New General Relativity

Abstract

We give an exact solution of the gravitational and electromagnetic field equations with a charged rotating source in new general relativity. The solution has three parameters Q, h and a, and it gives a charged Kerr metric space-time. The parallel vector fields and the electromagnetic vector poten-" tial are axially symmetric. In this 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 does not have singularities at all, although it has an "effective singularity". Two kinds of Reissner-Nordstrom 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 -+ 00 and the space-time singularities. *) This discussion can be easily extended to systems of the gravitational and scalar fields and of the gravitational and Yang-Mills fields. **) Note the following: (1) the curvature tensor of the Weitzenbock spacetime is vanishing. (2) The Riemann-Christoffel curvature tensor is not the curvature tensor of this space-time, but macroscopic test bodies "feel" effectively this curvature (see Ref. 2.