Global structure of the Zipoy Voorhees Weyl spacetime and the dgr = 2 Tomimatsu Sato spacetime
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 dgr = 2 Tomimatsu Sato spacetime. We show that the singularity of the ZVW spacetime, which is represented by a segment rgr = 0,  sgr < z < sgr in the Weyl coordinates, is geometrically pointlike for dgr < 0, stringlike for 0 < dgr < 1 and ringlike for dgr > 1. These singularities are always naked and have positive Komar masses for dgr > 0. Thus, they provide a nontrivial 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 dgr = 2, 3 and dgr geq 4. We also show that the dgr = 2 Tomimatsu Sato spacetime has a degenerate horizon with two components, in contrast to the general belief that the Tomimatsu Sato solutions with even dgr do not have horizons.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2003
 DOI:
 10.1088/02649381/20/23/011
 arXiv:
 arXiv:grqc/0304064
 Bibcode:
 2003CQGra..20.5121K
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 20 pages, 11 figures. The title was slightly changed, and references were added. The published version