Nakedness and curvature strength of a shell-focusing singularity in spherically symmetric spacetime with vanishing radial pressure

It was shown recently that the metric functions which describe a spherically symmetric spacetime with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that spacetime. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by R 2 y 0 m with (1/3)< 1 along the first radial null geodesic from the singularity. The 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) of Tipler holds, then 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) of Królak holds for = 1 and y 0 1, not SCC but only LFC holds for ½ <1, and neither holds for (1/3)< <½, 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 . Several examples are also discussed.