The role of the equation of state and the space-time dimension in spherical collapse

Abstract

We study the spherically symmetric collapse of a fluid with non-vanishing radial pressure in higher dimensional space-time. We obtain the general exact solution in the closed form for the equation of state ($P_r = γρ$) which leads to the explicit construction of the root equation governing the nature (black hole versus naked singularity) of the central singularity. A remarkable feature of the root equation is its invariance for the three cases: (${D+1}, {γ= -1}$), (${D}, {γ= 0}$) and (${D - 1}, {γ= 1}$) where $D$ is the dimension of space-time. That is, for the ultimate end result of the collapse, $D$-dimensional dust, ${D+1}$ - AdS (anti de Sitter)-like and ${D-1}$ - dS-like are absolutely equivalent.

4 Pages, RevTeX, no figures, minor changes, new references added, Detailed version to follow