Naked singularity formation in Brans–Dicke theory

Gravitational collapse of the Brans–Dicke scalar field with non-zero potential in the presence of matter fluid obeying the barotropic equation of state, p = w ρ, is studied. Utilizing the concept of the expansion parameter, it is seen that the cosmic censorship conjecture may be violated for and which correspond to the cosmic string and domain wall, respectively. We have shown that physically, it is the rate of collapse that governs the formation of a black hole or a naked singularity as the final fate of dynamical evolution and only for these two cases can the singularity be naked as the collapse end state. Also the weak energy condition is satisfied by the collapsing configuration.