Approximate form of the Tomimatsu–Sato δ=2 solution near the poles <i>x</i>=1, <i>y</i>=±1

Abstract

A consideration of the line element for the Tomimatsu–Sato δ=2 solution near the poles x=1, y=±1 reveals the existence of a metric which in nonsingular there. The further study of this metric indicates that it corresponds to a vacuum, type D gravitational field, and, as such, it is among those type D vacuum solutions specified by W. Kinnersley. Reasons are given in support of the belief that the derived metric is a valid approximation to the exact T–S solution close to the poles.