Abstract
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 four-dimensional (4D) Schwarzschild horizon in the Randall-Sundrum ${\mathrm{AdS}}_{5}$ 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 ${\mathrm{AdS}}_{5}$ horizon, such a tubular horizon is absent.
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