Kerr black holes as elementary particles

Long ago, Newman and Janis showed that a complex deformation z -> z + ia of the Schwarzschild solution produces the Long ago, Newman and Janis showed that a complex deformation z ! z + ia of the Schwarzschild solution produces the Kerr solution. The underlying explanation for this relationship has remained obscure. The complex deformation has an electromagnetic counterpart: by shifting the Coloumb potential, we obtain the EM field of a certain rotating charge distribution which we term p Kerr. In this note, we identify the origin of this shift as arising from the exponentiation of spin operators for the recently defined \minimally coupled three-particle amplitudes of spinning particles coupled to gravity, in the largespin limit. We demonstrate this by studying the impulse imparted to a test particle in the background of the heavy spinning particle. We first consider the electromagnetic case, where the impulse due to p Kerr is reproduced by a charged spinning particle; the shift of the Coloumb potential is matched to the exponentiated spin-factor appearing in the amplitude. The known impulse due to the Kerr black hole is then trivially derived from the gravitationally coupled spinning particle via the double copy.