  We examine the inclusion of brane self-gravity in brane-world scenarios with
three or more compact extra dimensions. If the brane is a thin, localized one,
then we find that the geometry in its vicinity is warped in such a way that
gravity on the brane can become very weak, independently of the volume of the
extra dimensions. As a consequence, self-gravity can make the brane structure
enter into the determination of the hierarchy between the Planck scale and a
lower fundamental scale. In an extreme case, one can obtain a novel
reformulation of the hierarchy problem in brane worlds, without the need for
large-size extra dimensions; the hierarchy would be generated when the ratio
between the scales of brane tension and brane thickness is large. In a sense,
such a scenario is half-way between the one of Arkani-Hamed et al.(ADD)
(although with TeV-mass Kaluza-Klein states) and that of Randall and Sundrum
(RS1) (but with only a TeV brane, and of positive tension). We discuss in
detail the propagation of fields in the background of this geometry, and find
that no problems appear even if the brane is taken to be very thin. We also
discuss the presence of black branes and black holes in this setting, and the
possibility of having a Planck brane.
