Quest for Localized 4-D Black Holes in Brane Worlds
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We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. It turns out that an exotic, shell-like distribution of matter is required. For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions.
17 pages, RevTex, 3 figures, version to appear in Physical Review D, comments and references added, typos corrected
17 pages, RevTex, 3 figures, version to appear in Physical Review D, comments and references added, typos corrected