We consider a static , axially symmetric , and asymptotically flat exact solution of the Einstein vacuum equations , known as the gamma metric .
This is characterized by two constant parameters m and \gamma .
We find that the total energy associated with this metric is m \gamma .
Considering the total energy to be positive , we investigate the nature of a curvature singularity r = 2 m ( r is the radial coordinate ) in this metric .
For \gamma < 1 , this singularity is globally visible along \theta = 0 as well as \theta = \pi / 2 .
However , for \gamma > 1 , this singularity is though globally naked along \theta = \pi / 2 , it is not visible ( even locally ) along \theta = 0 .
Thus , this exhibits “ directional nakedness ” for \gamma > 1 .
This could have implications for astrophysics .