Kerr Black Holes as Elementary Particles

Nima Arkani-Hamed, Yu-tin Huang, Donal O'Connell

Research output: Contribution to journalArticlepeer-review


Long ago, Newman and Janis showed that a complex deformation zz + 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 √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 √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.
Original languageEnglish
Article number46
Number of pages6
Journal Journal of High Energy Physics
Issue number1
Publication statusPublished - 8 Jan 2020


  • hep-th
  • gr-qc


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