Static Axially Symmetric Sources of the Gravitational Field

The gamma metric, a static axially symmetric vacuum solution of Einstein field equations, is reviewed, the nature of its singularity and the shape of its sources are studied. This space‐time is matched with an interior metric satisfying physically viable conditions. The model obtained, which can represent a dense astrophysical object, is used to investigate the boundary between black hole (i.e. Schwarzschild) and naked singularity as a function of the shape of the source.