It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated .
We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time .
If the singularity is naked , the relation between the circumferential radius and the Misner-Sharp mass is given by R \approx 2 y _ { 0 } m ^ { \beta } with 1 / 3 < \beta \leq 1 along the first radial null geodesic from the singularity .
The \beta is closely related to the curvature strength of the naked singularity .
For example , for the outgoing or ingoing null geodesic , if the strong curvature condition ( SCC ) by Tipler holds , then \beta must be equal to 1 .
We define the “ gravity dominance condition ” ( GDC ) for a geodesic .
If GDC is satisfied for the null geodesic , both SCC and the limiting focusing condition ( LFC ) by Królak hold for \beta = 1 and y _ { 0 } \neq 1 , not SCC but only LFC holds for 1 / 2 \leq \beta < 1 , and neither holds for 1 / 3 < \beta < 1 / 2 , for the null geodesic .
On the other hand , if GDC is satisfied for the timelike geodesic r = 0 , both SCC and LFC are satisfied for the timelike geodesic , irrespective of the value of \beta .
Several examples are also discussed .