Physical properties of the sources of the Gamma metric

A static axially symmetric vacuum solution of Einstein field equations, the so-called gamma metric, is reviewed and the nature of its singularity is studied. Given an interpretation of the parameters associated with the empty space metric, ways of building an interior solution are investigated. Finally a regular interior model matching the vacuum space-time is constructed and used to investigate the boundary between black hole (i.e. Schwarzschild) and naked singularity solution in dependence of the oblateness of the source.