What tells Gravity on the shape and size of an electron
  Gravitational field of an electron, fixed by experimental values of its mass, spin, charge and magnetic moment, is given by the metric of Kerr-Newman (KN) solution. Unexpectedly, this metric contains a singular ring of the Compton radius, which should be regulated resulting in a weeak and smooth source. The consistent source takes the form of an oblate vacuum bubble, bounded by a closed string of the Compton radius. The bubble turns out to be relativistically rotating and should be filled by a coherently oscillating Higgs field in a false vacuum state. 
Alexander Burinskii
physics.gen-ph gr-qc hep-ph