  We find a class of extremal black hole-like global p-brane in
higher-dimensional gravity with a negative cosmological constant. The region
inside the p-brane horizon possesses all essential features required for the
Randall-Sundrum-type brane world scenario. The set-up allows to interpret the
horizon size as the compactification size in that the Planck scale is
determined by the fundamental scale M* and the horizon size r_H via the
familiar relation M_Pl^2 ~ M*^{2+n} r_{H}^n, and the gravity behaves as
expected in a world with n-extra dimensions compactified with size r_H. Most
importantly, a stable mass hierarchy between M_Pl and M* can be generated from
topological charge of the p-brane and the horizon size r_H therein. We also
offer a new perspective on various issues associated to the brane world
scenarios including the cosmological constant problem.
