Role of Equation of State in formation of Black hole

We study the physical process of gravitational collapse of a perfect fluid with a linear isentropic equation of state $p=k\rho ,-1\mathrm{/}3<k\le 1$. We consider a model with ansatz $v^{\mathrm{\prime }}(t,r)\mathrm{/}v(t,r)={\xi }^{\mathrm{\prime }}(r)$ that give rise to a family of solutions to Einstein equations with equation of state. The solution so obtained lead to homogeneous collapse that evolves from a regular initial data and the positivity of energy conditions. The collapse terminates in the formation of black hole. We show that as the parameter $k\to 1$, the formation of black hole gets accelerated in time, revealing the significance of equation of state in black hole formation.