  A gravitational extension of Dirac's "Extensible model of the electron" is
presented. The Dirac bubble, treated as a 3-dim electrically charged brane, is
dynamically embedded within a 4-dim $Z_{2}$-symmetric Reissner-Nordstrom bulk.
Crucial to our analysis is the gravitational extension of Dirac's brane
variation prescription; its major effect is to induce a novel geometrically
originated contribution to the energy-momentum tensor on the brane. In turn,
the effective potential which governs the evolution of the bubble exhibits a
global minimum, such that the size of the bubble stays finite (Planck scale)
even at the limit where the mass approaches zero. This way, without
fine-tuning, one avoids the problem so-called 'classical radius of the
electron'.
