Role of the space-time dimensions & the fluid equation of state in spherical gravitational 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 (Pr = 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.