Dadhich, NareshDate, G.2012-03-122012-03-122000-07-14http://hdl.handle.net/11007/1283The Zipoy-Voorhees family of static, axisymmetric vacuum solutions orms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. We ana- yze some properties of the region near singularity by studying a natural amily of 2-surfaces. We establish that these have the topology of the 2-sphere by an application of the Gauss-Bonnet theorem. By computing he area, we establish that the singular region is ‘point-like’. Isometric mbedding of these surfaces in the three dimensional Euclidean space is used to distinguish the two types of deviations from spherical symmetry.enEinstein equationsStatic, Axisymmetric, Vacuum SolutionsPreprint