Graviton confinement inside hypermonopoles of any dimension

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.