Hoop Conjecture and Black Holes on a Brane

TL;DR

This paper investigates black hole formation in a brane-world scenario, showing that the hoop conjecture does not hold, as black holes can form without the matter being compacted into a small enough region.

Contribution

It demonstrates that in the Randall-Sundrum brane-world model, black holes can form from elongated matter distributions, challenging the traditional hoop conjecture.

Findings

Black holes can form from infinitely long matter configurations.

The hoop conjecture does not apply in the brane-world scenario.

Sufficiently thin matter distributions lead to marginal surface formation.

Abstract

The initial data of gravity for a cylindrical matter distribution confined to a brane are studied in the framework of the single-brane Randall-Sundrum scenario. In this scenario, the 5-dimensional nature of gravity appears in the short-range gravitational interaction. We find that a sufficiently thin configuration of matter leads to the formation of a marginal surface, even if the configuration is infinitely long. This implies that the hoop conjecture proposed by Thorne does not hold on the brane: Even if a mass $M$ does not become compacted into a region whose circumference ${\cal C}$ in every direction satisfies ${\cal C}> 4\pi GM$, black holes with horizons can form in the Randall-Sundrum scenario.