Global structure of the Zipoy-Voorhees-Weyl spacetime and the delta=2 Tomimatsu-Sato spacetime

TL;DR

This paper analyzes the geometric and singularity structures of the Zipoy-Voorhees-Weyl and delta=2 Tomimatsu-Sato spacetimes, revealing new insights into their naked singularities and horizon properties.

Contribution

It demonstrates that certain naked singularities in these spacetimes can have positive mass and uncovers the existence of degenerate horizons in delta=2 Tomimatsu-Sato spacetime, challenging previous assumptions.

Findings

Singularity types depend on delta: point-like, string-like, or ring-like.

Naked singularities with positive Komar mass are identified.

Delta=2 Tomimatsu-Sato spacetime has a degenerate horizon with two components.

Abstract

We investigate the structure of the ZVW (Zipoy-Voorhees-Weyl) spacetime, which is a Weyl solution described by the Zipoy-Voorhees metric, and the delta=2 Tomimatsu-Sato spacetime. We show that the singularity of the ZVW spacetime, which is represented by a segment rho=0, -sigma<z<sigma in the Weyl coordinates, is geometrically point-like for delta<0, string-like for 0<delta<1 and ring-like for delta>1. These singularities are always naked and have positive Komar masses for delta>0. Thus, they provide a non-trivial example of naked singularities with positive mass. We further show that the ZVW spacetime has a degenerate Killing horizon with a ring singularity at the equatorial plane for delta=2,3 and delta>=4. We also show that the delta=2 Tomimatsu-Sato spacetime has a degenerate horizon with two components, in contrast to the general belief that the Tomimatsu-Sato solutions with even delta do not have horizons.