2000/12/24 by Naresh Dadhich, N. Dadhich, Dadhich, N. +2
Mathematics · Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Theory of Mathematics #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0012093
12 pages, Latex, no figures
arxiv created 2000/12/24 · openalex publication_date 2000/12/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. We analyze some properties of the region near singularity by studying a natural family of 2-surfaces. We establish that these have the topology of the 2-sphere by an application of the Gauss-Bonnet theorem. By computing the area, we establish that the singular region is `point-like'. Isometric embedding of these surfaces in the three dimensional Euclidean space is used to distinguish the two types of deviations from spherical symmetry.