The hoop conjecture and cosmic censorship in the brane-world

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. We numerically found that the sufficiently thin configuration of matter leads to the formation of the marginal surface on the brane in the Randall–Sundrum model, 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 (C) in every direction is C≲4πGM, black holes with horizons can form on the brane-world of the Randall–Sundrum scenario.