Kerr-Newman from minimal coupling
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Springer
Received: October 9, 2019 Accepted: December 12, 2019 Published: January 3, 2020
Nathan Moynihan High Energy Physics, Cosmology & Astrophysics Theory group And The Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics, University Of Cape Town, Rondebosch, Cape Town 7700, South Africa
E-mail: [email protected] 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 ReissnerNordstr¨om 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. Keywords: Black Holes, Scattering Amplitudes ArXiv ePrint: 1909.05217
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)014
JHEP01(2020)014
Kerr-Newman from minimal coupling
Contents 1
2 Scattering amplitudes and spin operators
2
3 Tree-level leading singularity
4
4 One-loop leading singularity
6
5 Classical potential 5.1 Spin-independent potential 5.2 Spin-orbit potential 5.3 Infinite spin limit
9 10 11 12
6 Discussion
14
A Integral transforms A.1 Impulse Fourier transform A.2 Elliptical integrals
15 15 16
1
Introduction
Extracting classical gravitational physics from quantum field theories has a long history [2–4]. More recently the modern on-shell scattering amplitudes program has provided a number of tools that can be used to greatly simplify calculations of gravitational quantities, notably the KLT relations and the BCJ double copy [5–9], as well as those related specifically to classical observables [10–12]. While the original aim of the double copy program was to simplify loop computations in gravity, it has found many uses in classical gravity, from metric reconstruction [13–20] to gravitational wave physics [21–24]. In particular, the introduction of a formalism to compute amplitudes of arbitrary mass and spin [25] has provided a powerful way to investigate spin effects in classical observables [24, 26–29]. Calculations involving spin effects in gravity are often computed in the post-Newtonian (small velocities v c) or post-Minkowskian (expansion in G) frameworks [30–38], however there have also been calculations involving loop amplitudes via standard Feynman diagram techniques and form factors [39, 40]
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