Non-radial strong curvature naked singularities in five dimensional perfect fluid self-similar space-time

TL;DR

This paper investigates five-dimensional self-similar perfect fluid spacetimes, demonstrating the existence of strong curvature naked singularities that challenge cosmic censorship, and explores conditions for their visibility and strength.

Contribution

It presents a new analysis of 5D perfect fluid solutions with naked singularities and examines the role of energy conditions and matching to Schwarzschild spacetime.

Findings

Existence of globally strong curvature naked singularities in 5D

Weak energy condition necessary for singularity visibility

Matching of solutions to 5D Schwarzschild spacetime

Abstract

We study five dimensional(5D) spherically symmetric self-similar perfect fluid space-time with adiabatic equation of state, considering all the families of future directed non-spacelike geodesics. The space-time admits globally strong curvature naked singularities in the sense of Tipler and thus violates the cosmic censorship conjecture provided a certain algebraic equation has real positive roots. We further show that it is the weak energy condition (WEC) that is necessary for visibility of singularities for a finite period of time and for singularities to be gravitationally strong. We, also, match the solution to 5D Schwarzschild solution using the junction conditions.