High-speed collapse of a hollow sphere of type I matter

Abstract

In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure p R = kρ and tangential one p T = wρ with constant k and w are assumed. We find for the case of equations of state k < 1 and 0 < w ≤ 1 that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of w < −(1 − k)/4, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime.

Gravitational Collapse with Cosmological Constant and Anisotropic Pressure

“…Charged cylindrical collapse with anisotropic pressure was studied Sharif and Fatima [27]. Ahmad et al [28] discussed the high speed spherical collapse with anisotropic pressure. Using high-speed approximation scheme the cylindrical symmetric gravitational collapse with anisotropic pressure was studied by Ahmad and Imtiaz [29].…”

High-Speed Cylindrical Collapse of Type-I Matter

“…Herrera and Santos [41] have investigated cylindrical gravitational collapse with anisotropic pressure using matching conditions. Ahmad et al [42] investigated high-speed spherical collapse of type-I matter with some interesting results. Motivated by these studies, we investigate the cylindrical gravitational collapse with anisotropic pressure using highspeed approximation in this paper.…”

High Speed Cylindrical Gravitational Collapse with Anisotropic Pressure

“…Ahmad et al [35] have discussed spherical collapse using a high speed approximation scheme in the background of anisotropic matter with some useful results. Ahmad and Imtiaz [26] extended this work for cylindrically symmetric spacetime.…”