The Effect of Pressure in Higher Dimensional Quasi-Spherical Gravitational Collapse

Abstract

We study gravitational collapse in higher dimensional quasi-spherical Szekeres space-time for matter with anisotropic pressure. Both local and global visibility of central curvature singularity has been studied and it is found that with proper choice of initial data it is possible to show the validity of CCC for six and higher dimensions. Also the role of pressure in the collapsing process has been discussed.

Optimizing system performance in the event of feedback failure

“…A bang-bang function is a function whose component values switch between the bound values ±K of the system's input; such a function is completely determined by its switching times. The following statement shows that performance close to optimal performance can be achieved by using a bang-bang input function (see [5] for proof). As the deviation δ from optimal performance can be selected as small as desired, it follows that a bang-bang input signal can always be used without incurring a significant penalty on performance.…”

“…The cost of making δ smaller is an increase in the number of switches of the bang-bang input function u ± δ . A more detailed discussion of the results presented in this note, including proofs and numerical examples, is provided in [5].…”

“…This leads us to introduce the set of input functions U := {u(t) : ||u(t)|| ≤ K for all t > 0}, which describes all permissible input functions of Σ. Discussion of the topology of the space within which U resides are omitted in this brief note (see [5]). …”

Dynamics of charged plane symmetric gravitational collapse

“…The phenomenon of gravitational collapse has also been explored in the context of cylindrical, planar and quasi-spherical symmetries [14]- [19]. Kurita and Nakao [20] studied the null dust collapse for the cylindrically symmetric spacetimes.…”