High-Speed Cylindrical Collapse of Type-I Matter

In this paper, the cylindrical symmetric gravitational collapse with anisotropic pressure has been investigated using high-speed approximation scheme. The collapsing speed of the fluid is assumed to be very large. To see the effects of pressure, we have used the equations $ \sqrt{p_{R}/\rho}=k$ and $\sqrt{p_{T}/\rho}=w$ of states for radial pressure and tangential pressure, respectively. It is observed that if the ratios of both pressures, that is, tangential and radial pressures, to energy density are bounded from below by some positive value, there arise two possibilities depending on whether 1?+?k ²???2 w ²?>?0 or 1?+?k ²???2w ²?<?0. For 1?+?k ²???2 w ²?>?0, the high-speed approximation scheme fails, while for 1?+?k ²???2 w ²?<?0, the high-speed approximation works. For vanishing w and k, the high-speed scheme does not break down, and, as a result, a naked singularity forms in this case. For p _T ?=?p _R ?=?p, all the results reduce to the perfect fluid case obtained by Nakao and Morisawa (Prog Theor Phys 113:73, 2005).