Kerr black holes as elementary particles

• Published in: The journal of high energy physics Vol. 2020; no. 1; pp. 1 - 12
• Main Authors: Arkani-Hamed, Nima, Huang, Yu-tin, O’Connell, Donal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Amplitudes; Black Holes; Charge distribution; Charged particles; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Scattering Amplitudes; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2020)046

A bstract 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 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.