Hoop Conjecture and Black Holes on a Brane

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.Comment: 7 pages, 1 figure, To be published in Progress of Theoretical Physics Supplement No. 148 "Brane World: New Perspective in Cosmology