We analyse here the gravitational collapse of directed null radiation in a
background with a constant potential such as one produced by a star system like
galaxy in which the collapsing object is immersed. Both naked singularities and
black holes are shown to be developing as the final outcome of the collapse. An
interesting feature that emerges is that a part of the naked singularity
spectrum in collapsing Vaidya region gets covered in the corresponding
dual-Vaidya region, which corresponds to the Vaidya directed null radiation
sitting in constant potential bath. The implications of such a result towards
the issue of stability of naked singularities are discussed.Comment: LaTex 12 Pages, 2 figures. To appear in Physical Review
