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

Naresh Dadhich·S. G. Ghosh·D. W. Deshkar
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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.

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Naresh Dadhich, S. G. Ghosh, D. W. Deshkar. 2003-05-30. The role of the equation of state and the space-time dimension in spherical collapse. https://doi.org/10.1142/s0217751x05021038

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