Possible Extensions of the 4-d Schwarzschild Horizon in the Brane World

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 4-D Schwarzschild horizon in the Randall-Sundrum $Ad{S}_5$ 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 $Ad{S}_5$ horizon, such a tubular horizon is absent.

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