Kerr-Newman from minimal coupling

Abstract

We show that at 1PN all four-dimensional black hole solutions in asymptotically flat spacetimes can be derived from leading singularities involving minimally coupled three-particle amplitudes. Furthermore, we show that the rotating solutions can be derived from their non-rotating counterparts by a spin-factor deformation of the relevant minimally coupled amplitudes. To show this, we compute the tree-level and one-loop leading singularities for a heavy charged source with generic spin s. We compute the metrics both with and without a spin factor and show that we get both the Kerr-Newman and Reissner-Nordström solutions respectively. We then go on to compute the impulse imparted to the probe particle in the infinite spin limit and show that the spin factor induces a complex deformation of the impact parameter, as was recently observed for Kerr black holes in [1]. We interpret these observations as being the on-shell avatar of the Janis-Newman algorithm for charged black holes.

The classical double copy of a point charge

“…This property was instrumental in interpreting the exact solution as the double copy of a point charge in [5], and this conclusion extends to many other cases, including the Kerr and Taub-NUT metrics -in fact, it extends to all vacuum type D spacetimes [15]. This double-copy interpretation is further supported by more recent arguments involving solution-generating techniques, computations with scattering amplitudes, duality considerations, and asymptotic symmetries [20,64,66,69,72]. Notice that, in terms of the 'fat graviton' (2.9), the Schwarzschild case (Y = 0) does not look particularly simple.…”

Double copy of electric-magnetic duality

“…It would be interesting to verify this conjectural link to Kerr-Taub-NUT by comparing the classical linear and angular impulses with those computed via geodesic equations, utilizing the simplifications in the post-Minkowskian expansion discussed in this paper. As a further step, one could consider solutions of the combined Einstein-Maxwell equations which again connect to minimally coupled scattering amplitudes [5]. Indeed considerations from the Weyl spinor formulation of the classical double copy [40] suggest that similar ideas apply to the full Plebanski-Demianski [7,8] class of solutions, which include not only spin, electric and magnetic charges, masses, and NUT parameters, but also an acceleration parameter as well as a cosmological constant.…”

“…Similarly, the Taub-NUT metric is described by just two quantum numbers: the mass and the NUT charge. Indeed, it was recently shown that the effective stress-energy tensor for the Kerr and the Kerr-Newman black holes are given by the classical-spin limit of minimally coupled (charged) spinning particles [3,[28][29][30]; see also [5]. Note that while a consistent description of isolated higher spin particles beyond spin 2 is not known, the notion of minimal coupling at three points can be defined in a purely kinematic fashion [31].…”

“…This complex shift was also shown to be related by the double copy 1 structure, which identifies solutions of the Einstein equations as the square of Yang-Mills gauge theory solutions, to a similar exponentiation of spin operators in the minimal coupling of spinning particles to a photon. More generally, the Newman-Janis link between the Reissner-Nordström and Kerr-Newman black holes was also connected to minimal coupling and spinning particles [5].…”

Test black holes, scattering amplitudes, and perturbations of Kerr spacetime

“…It was shown in [53] through O(a 2 ), and then by Ochirov et al in [54] through O(a ∞ ) for both spins, that the arbitrary-spin tree amplitudes from [40,42,43] lead (by a well-motivated procedure) to the covariant scattering holonomy results for genericspin binary BHs at O(G 1 a ∞ ) derived by one of the authors in [15], matching at O(G 1 a 1 ) results of Bini and Damour [10]. A scalar-probe limit of the same genericspin scattering holonomy, namely the O(G 1 a ∞ ) impulse (change in momentum) for a generic (weakly deflected) unbound geodesic in the Kerr spacetime, has also been produced from an elegant double copy of the amplitude for the analogous electromagnetic case, a test charge in the " √ Kerr " electromagnetic field in flat spacetime, by Arkani-Hamed, Huang and O'Connell [55]; see also [56]. Further perspectives on higher-spin-multipole effects along with double-copy constructions have been given by Johansson and Ochirov [57], as well as by Bautista and Guevara [58,59] who also discussed the structure of radiative amplitudes with spin effects.…”