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We propose an approach for constructing spatial slices of (3+1) spacetimeswith cosmological constant but without a matter content, which yields (2+1)vacuum with $\Lambda$ solutions. The reduction mechanism from (3+1) to (2+1)gravity is supported on a criterion in which the Weyl tensor components arerequired to vanish together with a dimensional reduction via an appropriatefoliation. By using an adequate reduction mechanism from thePleba\'nski-Carter[A] solution in (3+1) gravity, the (2+1) BTZ solution can beobtained.Comment: 4 pages, Late

LETTER: BTZ Black Hole from (3+1) Gravity