We consider the chiral field model of the source of the Kerr–Newman (KN) solution and obtain that it represents a supersymmetric spinning soliton, bounded by the chiral domain wall (DW) of the ellipsoidal form. The known method for transformation of the planar DW to Bogomolnyi form we generalize to the curved DW-bubble adapted to the Kerr coordinate system and obtain the supersymmetric BPS-saturated source of the KN solution, having some remarkable features, in particular, the quantum angular momentum. The main new result is that the source forms a breather, i.e. the DW–antiDW combination. Taking into account that the KN solution describes the spinning particles with gyromagnetic ratio , as that of the Dirac electron, we touch the problem of the compatibility of the spinning particles with gravity.
