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Amplitudes from Coulomb to Kerr-Taub-NUT

William T. Emond, Yu-tin Huang, Uri Kol, Nathan Moynihan, Donal O'Connell

TL;DR

The paper builds a unified framework linking electric–magnetic duality, the Newman–Janis shift, and the double copy to a network of classical solutions ranging from Coulomb to Kerr–Taub–NUT, all encoded by simple three-point amplitudes. By working in linearised gravity and summing to all orders in spin, the authors derive compact, phase-encoded amplitudes for each node of an eight-solution cube and verify the classical double copy by matching impulses computed both from geodesic/electromagnetic methods and from on-shell amplitudes. They show that Kerr–Taub–NUT is obtained from Kerr via a gravitational duality, with mass and NUT charge rotating into each other, and that the corresponding amplitudes double-copy to reproduce the gravitational impulse from the gauge-theory result. The work provides strong evidence for the Weyl double copy and elucidates how asymptotic charges transform under these operations, offering a concrete, amplitude-based testbed for all-orders-in-spin and potential extensions to higher orders. The results pave the way for broader applications of amplitudes to classical gravity and highlight the deep role of symmetry operations in connecting disparate solutions.

Abstract

Electric-magnetic duality, the Newman-Janis shift, and the double copy all act by elementary operations on three-point amplitudes. At the same time, they generate a network of interesting classical solutions spanning from the Coulomb charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes corresponding to each of these solutions, working to all orders in spin, but to leading perturbative order. We confirm that the amplitudes double-copy when the solutions are related by the classical double copy. Along the way we show that the Kerr-Taub-NUT solution corresponds to a gravitational electric-magnetic duality rotation acting on the Kerr solution, again to all orders in spin, and demonstrate that the asymptotic charges also transform simply under our operations.

Amplitudes from Coulomb to Kerr-Taub-NUT

TL;DR

The paper builds a unified framework linking electric–magnetic duality, the Newman–Janis shift, and the double copy to a network of classical solutions ranging from Coulomb to Kerr–Taub–NUT, all encoded by simple three-point amplitudes. By working in linearised gravity and summing to all orders in spin, the authors derive compact, phase-encoded amplitudes for each node of an eight-solution cube and verify the classical double copy by matching impulses computed both from geodesic/electromagnetic methods and from on-shell amplitudes. They show that Kerr–Taub–NUT is obtained from Kerr via a gravitational duality, with mass and NUT charge rotating into each other, and that the corresponding amplitudes double-copy to reproduce the gravitational impulse from the gauge-theory result. The work provides strong evidence for the Weyl double copy and elucidates how asymptotic charges transform under these operations, offering a concrete, amplitude-based testbed for all-orders-in-spin and potential extensions to higher orders. The results pave the way for broader applications of amplitudes to classical gravity and highlight the deep role of symmetry operations in connecting disparate solutions.

Abstract

Electric-magnetic duality, the Newman-Janis shift, and the double copy all act by elementary operations on three-point amplitudes. At the same time, they generate a network of interesting classical solutions spanning from the Coulomb charge via the dyon to the Kerr-Taub-NUT spacetime. We identify the amplitudes corresponding to each of these solutions, working to all orders in spin, but to leading perturbative order. We confirm that the amplitudes double-copy when the solutions are related by the classical double copy. Along the way we show that the Kerr-Taub-NUT solution corresponds to a gravitational electric-magnetic duality rotation acting on the Kerr solution, again to all orders in spin, and demonstrate that the asymptotic charges also transform simply under our operations.

Paper Structure

This paper contains 18 sections, 175 equations, 4 figures.

Table of Contents

  1. Introduction
  2. A Network of Solutions
  3. Newman-Penrose and Asymptotic Charges
  4. Spinning Dyons from Duality
  5. Kerr-Taub-NUT from Duality
  6. The Impulse
  7. Spinning Dyon
  8. Kerr-Taub-NUT
  9. Geodesics
  10. A Network of Amplitudes
  11. Connecting Amplitudes to Solutions
  12. Electromagnetic Impulses from Amplitudes
  13. Gravitational Impulses from Amplitudes
  14. Discussion
  15. Conventions
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Classical solutions related by the double copy (dashed blue arrow), duality (green arrow) and the Newman-Janis shift (orange arrow). The double copy provides a map between solutions of different theories. Duality and the Newman-Janis shift, on the other hand, map different solutions within the same theory and depend on continuous parameters.
  • Figure 2: Three-particle amplitudes related by the double copy (dashed blue arrow), duality (green arrow) and the Newman-Janis shift (orange arrow). For brevity, throughout the paper we have rescaled the gravitational phase factors by a factor of half.
  • Figure 3: Electromagnetic probe of a charged, spinning particle
  • Figure 4: Gravitational probe of a charged, spinning particle