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We show that, in the absence of matter in the bulk, the Einstein equationsand the Gauss-normal form of the metric place stringent restrictions on theform of the event horizon in a brane world. As a consequence, the off-braneextension of the standard 4-D Schwarzschild horizon in the Randall-Sundrum$AdS_5$ spacetime, as it is viewed from the brane can only be of a tubularshape, instead of a pancake shape. When it is viewed from the $AdS_5$ horizon,such a tubular horizon is absent.Comment: Minor changes, new references added, 10 pages, 1 figure, Plain Te

Possible extensions of the 4D Schwarzschild horizon in the 5D brane world