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We study the physical process of gravitational collapse of a perfect fluidwith a linear isentropic equation of state $p = k \rho, \ -1/3 < k \leq 1$. Weconsider a model with ansatz $v'(t,r)/v(t,r) = \xi'(r)$ that give rise to afamily of solutions to Einstein equations with equation of state. The solutionso obtained lead to homogeneous collapse that evolves from a regular initialdata and the positivity of energy conditions. The collapse terminates in theformation of black hole. We show that as the parameter $k \rightarrow 1$, theformation of black hole gets accelerated in time, revealing the significance ofequation of state in black hole formation.

Role of Equation of State in formation of Black hole