Higher dimensional dust collapse with a cosmological constant

Abstract

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.

Quasi-spherical solution with heat flux and non-adiabatic collapse of radiating star

“…which is identical in form to the earlier works of Santos et al [4,5] and Ghosh et al [11]. Also the other conclusions are very much similar to their results.…”

“…From equations (4) and (5) using equations (11) and (12) we have the differential equations for R and D:…”

“…Since then several authors have extended the above study of collapse of which important and realistic generalizations are the following: (i) the static exterior was studied by Misner and Sharp [2] for a perfect fluid in the interior, (ii) using the idea of outgoing radiation of the collapsing body by Vaidya [3], Santos and collaborations [4][5][6][7][8][9] included the dissipation in the source by allowing radial heat flow (while the body undergoes radiating collapse). Recently, Ghosh and Deskar [10] have considered collapse of a radiating star with a plane symmetric boundary (which has a close resemblance with spherical symmetry [11]) and have concluded with some general remarks.…”

The Cosmic Censorship Conjecture in a Higher Dimensional Spacetime and Λ

“…Presently, we do not have a satisfactory mathematical formulation of CCC available, but we have in scientific literature several counterexamples, besides of the above cited, where the integration of the Einstein field equations result solutions which admit naked singularities. See for example the references [7][8][9][10][11].…”

Gravitational collapse: expanding and collapsing regions

“…Debnath et al [17] explored the quasispherical collapse with cosmological constant by using the Israel junction conditions modified by Santos. Ghosh and Deshkar [18] discussed the higher dimensional spherically symmetric dust collapse. Sharif and Ahmad [19][20][21] extended the spherically symmetric gravitational collapse with positive cosmological constant for perfect fluid.…”