2019/06/30 by Nima Arkani-Hamed, Yu-tin Huang, Donal O'Connell · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1007/jhep01(2020)046
6 pages 1 figure V2. minor corrections, published version
arxiv created 2020/01/04 · arxiv updated 2020/01/29
Long ago, Newman and Janis showed that a complex deformation z→ z+i a 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 √(\rm 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 large-spin 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 √(\rm 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.