High-Speed Cylindrical Collapse of Two Perfect Fluids

Abstract

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by $c_s,d_s$. It is shown that the high-speed approximation scheme breaks down by non-zero pressures $p_1,p_2$ when $c_s,d_s$ are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainity on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa [1] for the perfect fluid.

11 pages, 1 figure, accepted for publication in Gen. Rel. Grav

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• Gravitational collapse of cylindrical anisotropic fluid: A source of gravitational waves
• Gravitational Collapse and Expansion of Charged Anisotropic Cylindrical Source
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• High-Speed Collapse of a Hollow Sphere of Type I Matter
• Gravitational collapse of dissipative fluid as a source of gravitational waves
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• Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime
• Collapsing Plane Symmetric Source with Heat Flux and Conformal Flatness