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 $Λ$. The corresponding density function $ρ(a)$ 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 $0\, \leΛ< 1$, 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 $Λ$, the singularity formation time, $t_s$ increases. For $Λ= 1$, we obtain $a(t) = 0$, thus limiting the maximum value of $Λ$, (w.r.t the initial density $ρ_0$) for which the system could collapse under gravity.

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