Conformal symmetries in generalised Vaidya spacetimes

In this paper we generate, for the first time, the most general class of conformal Killing vectors, that lies in the two dimensional subspace described by the null and radial coordinates, that are admitted by the generalised Vaidya geometry. Subsequently we find the most general class of generalised Vaidya mass functions that give rise to such conformal symmetry. From our analysis it is clear that why some well known subclasses of generalised Vaidya geometry, like pure Vaidya or charged Vaidya solutions, admit only homothetic Killing vectors but no proper conformal Killing vectors with non-constant conformal factors. We also study the gravitational collapse of generalised Vaidya spacetimes that possess proper conformal symmetry to show that if the central singularity is naked then in the vicinity of the central singularity the spacetime becomes almost self-similar. This study definitely sheds new light on the geometrical properties of generalised Vaidya spacetimes.