Black Objects and Hoop Conjecture in Five-dimensional Space-time

TL;DR

This paper uses numerical methods to study the formation of black holes and black rings in five-dimensional space-time, testing the hyper-hoop conjecture and exploring conditions for naked singularities.

Contribution

It provides the first numerical analysis of initial data sequences for black objects in five dimensions, examining horizon formation and the validity of the hyper-hoop conjecture.

Findings

Black hole and black ring horizons form under specific conditions.

Naked singularities or rings may appear in certain scenarios.

The hyper-hoop conjecture does not always predict horizon formation accurately.

Abstract

We numerically investigated the sequences of initial data of thin spindle and thin ring in five-dimensional space-time in the context of the cosmic censorship conjecture. We modeled the matter in non-rotating homogeneous spheroidal or toroidal configurations under the momentarily static assumption, solved the Hamiltonian constraint equation, and searched the apparent horizons. We discussed when $S^3$ (black hole) or $S^1 \times S^2$ (black ring) horizons ("black objects") are formed. By monitoring the location of the maximum Kretchmann invariant, an appearance of `naked singularity' or `naked ring' under special situation is suggested. We also discuss the validity of the {\it hyper-hoop} conjecture using minimum {\it area} around the object, and show that the appearance of the ring horizon does not match with this hoop.