Gravitational Collapse of Massless Vector Field with Positive Cosmological Constant

We investigate the dynamics of homogeneous gravitational collapse of a massless vector field in the presence of a positive cosmological constant $\Lambda$. The corresponding density function $\rho (a)$ obtained for the massless vector field is inversely proportional to the fourth power of the scale factor $a (t)$. The variation of the scale factor shows that for $0\, \le\Lambda < 1$, we obtain the gravitational collapse of the vector fields leading singularity formation in a {\it finite} comoving time resulting in a {\it Blackhole} such that with increasing $\Lambda$, the singularity formation time, $t_s$ increases. For $\Lambda = 1$, we obtain $a(t) = 0$, thus limiting the maximum value of $\Lambda$, (w.r.t the initial density $\rho_0$) for which the system could collapse under gravity.