On the physical interpretation of the delta=2 Tomimatsu-Sato solution

TL;DR

This paper investigates the physical characteristics of the delta=2 Tomimatsu-Sato spacetime, focusing on negative mass effects and singularities, and relates these findings to the extended double-Kerr solution framework.

Contribution

It provides an analytical analysis of negative mass distributions and singularities in the delta=2 Tomimatsu-Sato spacetime, linking them to the extended double-Kerr solution.

Findings

Negative mass in Kerr spacetime leads to a naked ring singularity.

The delta=2 Tomimatsu-Sato spacetime exhibits negative mass regions and a massless ring singularity.

Boyer-Lindquist coordinates require modification for negative mass Kerr solutions.

Abstract

The physical properties of the Tomimatsu-Sato delta=2 spacetime are analyzed, with emphasis on the issues of the negative mass distribution in this spacetime and the origin of a massless ring singularity which are treated with the aid of an equatorially asymmetric two-body configuration arising within the framework of the analytically extended double-Kerr solution. As a by-product of this analysis it is proved analytically that the Kerr spacetime with negative mass always has a massless naked ring singularity off the symmetry axis accompanied by a region with closed timelike curves, and it is also pointed out that the Boyer-Lindquist coordinates in that case should be introduced in a different manner than in the case of the Kerr solution with positive mass.