Group Transformation That Generates the Kerr and Tomimatsu-Sato Metrics

Abstract

For stationary axially symmetric vacuum metrics, we give a series of transformations ${\ensuremath{\beta}}^{(k)}$ which automatically preserve asymptotic flatness. We show how to generate the Kerr metric from the Schwarzschild, using ${\ensuremath{\beta}}^{(0)}$. We also show, using ${\ensuremath{\beta}}^{(k)}$, that the Tomimatsu-Sata (TS) class of metrices must be larger than previously realized, and for $\ensuremath{\delta}=2$ there is a five-parameter TS metric. As an example, we present a two-parameter metric from this family, which we claim to be a new, physically realistic, asymptotically flat, rotating vacuum solution.