Kerr Black Holes as Elementary Particles

Abstract

Long ago, Newman and Janis showed that a complex deformation $z\to z+ia$ 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 $\sqrt{\mathrm{Kerr}}$. 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 $\sqrt{\mathrm{Kerr}}$ 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.

arXiv comment6 pages 1 figure V2. minor corrections, published version

References in corpus (18)

• General relativity as an effective field theory: The leading quantum corrections
• Leading Quantum Correction to the Newtonian Potential
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Black holes and the double copy
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• The classical double copy for Taub-NUT spacetime
• Quantum Corrections to the Schwarzschild and Kerr Metrics
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• The simplest massive S-matrix: from minimal coupling to Black Holes
• On Post-Minkowskian Hamiltonians in General Relativity
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Classical Physics and Quantum Loops
• Quantum Corrections to the Reissner-Nordström and Kerr-Newman Metrics
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO

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