  We show that, in the absence of matter in the bulk, the Einstein equations
and the Gauss-normal form of the metric place stringent restrictions on the
form of the event horizon in a brane world. As a consequence, the off-brane
extension 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 tubular
shape, instead of a pancake shape. When it is viewed from the $AdS_5$ horizon,
such a tubular horizon is absent.
