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We study the complete gravitational collapse of a class of sphericallysymmetric inhomogeneous perfect fluid models obtained by introducing smallradial perturbations in an otherwise homogeneous matter cloud. Our aim here isto study the genericity and stability of the formation of black holes andlocally naked singularities in collapse. While the occurrence of nakedsingularities is known for many models of collapse, the key issue now in focusis genericity and stability of these outcomes. Towards this purpose, we studyhow the introduction of a somewhat general class of small inhomogeneities inhomogeneous collapse leading to a black hole can change the final outcome to anaked singularity. The key feature that we assume for the perturbation profileis that of a mass profile that is separable in radial and temporal coordinates.The known models of dust and homogeneous perfect fluid collapse can be obtainedfrom this choice of the mass profile as special cases. This choice is verygeneral and physically well motivated and we show that this class of collapsemodels leads to the formation of a naked singularity as the final state.

Genericity aspects of black hole formation in the collapse of spherically symmetric slightly inhomogeneous perfect fluids