Hoop Conjecture and Cosmic Censorship in the Brane-World

TL;DR

This paper investigates gravitational collapse in a brane-world model, showing that black holes can form without the matter being compacted into a small enough region, challenging the hoop conjecture.

Contribution

It demonstrates that the hoop conjecture does not hold in the Randall-Sundrum brane-world scenario, revealing new insights into black hole formation in higher-dimensional gravity.

Findings

Black holes can form from infinitely long matter configurations.

The hoop conjecture is violated in the Randall-Sundrum scenario.

Sufficiently thin matter configurations lead to horizon formation.

Abstract

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