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 ($P_r=\gamma \rho$) 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: ($D+1,\gamma =-1$), ($D,\gamma =0$) and ($D-1,\gamma =1$) 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.

arXiv comment4 Pages, RevTeX, no figures, minor changes, new references added, Detailed version to follow

References in corpus (13)

• A Large Mass Hierarchy from a Small Extra Dimension
• Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse
• On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust
• Final fate of the spherically symmetric collapse of a perfect fluid
• On naked singularities in higher dimensional Vaidya space-times
• Naked singularity formation in the collapse of a spherical cloud of counterrotating particles
• Higher dimensional inhomogeneous dust collapse and cosmic censorship
• Negative Pressure and Naked Singularities in Spherical Gravitational Collapse
• Black holes vs. naked singularities formation in collapsing Einstein's clusters
• Gravitational collapse of Type II fluid in higher dimensional space-times
• Gravitational Collapse of Perfect Fluid
• Singularities in gravitational collapse with radial pressure
• Gravitational Collapse of Perfect Fluid in N-Dimensional Spherically Symmetric Spacetimes

Cited by in corpus (6)

• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• Bardeen-like regular black holes in $5D$ Einstein-Gauss-Bonnet gravity
• Is cosmic censorship restored in higher dimensions?
• Charged compact star model in Einstein-Maxwell-Gauss-Bonnet gravity
• Spherically symmetric solutions and gravitational collapse in brane-worlds
• The effect of loop quantum gravitational rainbow functions on the formation of naked singularities