  We show the generic existence of metastable massive gravitons in the
four-dimensional core of self-gravitating hypermonopoles in any number of
infinite-volume extra-dimensions. Confinement is observed for Higgs and gauge
bosons couplings of the order unity. Provided these resonances are light
enough, they realise the Dvali-Gabadadze-Porrati mechanism by inducing a
four-dimensional gravity law on some intermediate length scales. The effective
four-dimensional Planck mass is shown to be proportional to a negative power of
the graviton mass. As a result, requiring gravity to be four-dimensional on
cosmological length scales may solve the mass hierarchy problem.
