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, $p=w\rho$ is studied. Utilizing the concept of expansion parameter, it is seen that the cosmic censorship conjecture may be violated for $w=-\frac{1}{3}$ and $w=-\frac{2}{3}$ which correspond to cosmic string and domain wall, respectively. We show that physically, it is the rate of collapse and the presence of Brans-Dicke scalar field that govern the formation of a black hole or a naked singularity as the final fate of dynamical evolution and only for these two cases the singularity can be naked as the collapse end state. Also the weak energy condition is satisfied by the collapsing configuration.