N-dimensional gravitational collapse of Type I matter fields with non-zero radial pressure

TL;DR

This paper investigates how the dimensionality of spacetime influences gravitational collapse outcomes of Type I matter fields with radial pressure, revealing naked singularities in lower dimensions and censorship in higher ones.

Contribution

It demonstrates the dimensional dependence of naked singularity formation in N-dimensional gravitational collapse with radial pressure, extending previous four-dimensional results.

Findings

Naked singularities occur in 4 and 5 dimensions.

For N ≥ 6, Cosmic Censorship holds.

Naked singularities also appear with linear equations of state across all dimensions.

Abstract

We study the gravitational collapse of Type I matter field in $N$ dimensional spacetime with radial pressure $p_{r}$ as a function of $r $. We find that for a given smooth initial data set satisfying physical requirements, naked singularities exist for spacetime dimensions N=4 and 5 while for $N \geq 6$ Cosmic Censorship Conjecture withholds its ground. We, also, study the collapse with linear equation of state and find that, similar to dust collapse with appropriate choice of initial data naked singularities occur in all dimensions.