Gravitational collapse of Vaidya spacetime

The gravitational collapse of generalized Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M ( v , r ) . Here we give conditions for the mass function which corresponds to the equation of the state P = α ρ where α ∈ ( 0 , 1 3 ] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong.