We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin <math><mi>S</mi></math>. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the <math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math> quadratic-in-spin two-body Hamiltonian. We first evaluate the <math><msup><mi>S</mi><mn>3</mn></msup></math> scattering angle and two-body Hamiltonian at this order in <math><mi>G</mi></math>, including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate <math><msup><mi>S</mi><mn>4</mn></msup></math> and <math><msup><mi>S</mi><mn>5</mn></msup></math> contributions at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></math> which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously obtained results through <math><msup><mi>S</mi><mn>4</mn></msup></math>.

United States

Zvi Bern

Dimitrios Kosmopoulos

Denmark

Andrés Luna

Radu Roiban

Fei Teng

Binary Dynamics through the Fifth Power of Spin at <math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math>

The classical double copy relates solutions of biadjoint, gauge, and gravity theories. The ultimate origin and scope of this correspondence remains mysterious, such that it is important to build a clear physical intuition of how the double copy operates. To this end, we consider the multipole expansion of exact classical solutions. Using a recently developed twistor translation of the classical double copy, we use well-established techniques to show that the multipole moments of arbitrary vacuum type-D gravity fields are exactly related to their counterparts in gauge and biadjoint scalar theories by the single and zeroth copies. We cross-check our results using previously obtained results for the Kerr metric and also provide new results for the “square root” of the Kerr-Taub-NUT solution.

United Kingdom

Erick Chacón

Chris D. White

Double copy of the multipole expansion

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

Mexico

Hugo García-Compeán

Ricardo Monteiro

Chris White

New heavenly double copies

The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this to a particular example, namely the point charge in pure gauge theory. As well as clarifying how to use the convolutional approach, our results provide an alternative point of view on a recent discussion concerning whether point charges map to the Schwarzschild solution, or the more general two-parameter JNW solution, which includes a dilaton field. We confirm the latter.

Silvia Nagy

The convolutional double copy: a case study with a point

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for <math><mn>2</mn><mo>→</mo><mn>2</mn></math> scattering in <math><mi>N</mi><mo>=</mo><mn>8</mn></math> supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational S-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.

Sweden

Paolo Di Vecchia

Stephen G. Naculich

Rodolfo Russo

CERN

France

Gabriele Veneziano

A tale of two exponentiations in Supergravity

The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gauge field thus obtained represents an abelian-like object whose field is dipole-like at large distances, and which has no magnetic or electric charge.

David Berman

The self-dual classical double copy, and the Eguchi-Hanson instanton

We explain how the lowest-order classical gravitational radiation produced during the inelastic scattering of two Schwarzschild black holes in General Relativity can be obtained from a tree scattering amplitude in gauge theory coupled to scalar fields. The gauge calculation is related to gravity through the double copy. We remove unwanted scalar forces which can occur in the double copy by introducing a massless scalar in the gauge theory, which is treated as a ghost in the link to gravity. We hope these methods are a step towards a direct application of the double copy at higher orders in classical perturbation theory, with the potential to greatly streamline gravity calculations for phenomenological applications.

Isobel Nicholson

Donal O’Connell

Inelastic black hole scattering from charged scalar amplitudes

The double copy is a much-studied relationship between scattering amplitudes in gauge and gravity theories, that has subsequently been extended to classical field solutions. In nearly all previous examples, the graviton field is defined around Minkowski space. Recently, it has been suggested that one may set up a double copy for gravitons defined around a non-trivial background. We investigate this idea from the point of view of the classical double copy. First, we use Kerr-Schild spacetimes to construct graviton solutions in curved space, as double copies of gauge fields on non-zero gauge backgrounds. Next, we find that we can reinterpret such cases in terms of a graviton on a non-Minkowski background, whose single copy is a gauge field in the same background spacetime. The latter type of double copy persists even when the background is not of Kerr-Schild form, and we provide examples involving conformally flat metrics. Our results will be useful in extending the remit of the double copy, including to possible cosmological applications.

Nadia Bahjat-Abbas

The Kerr-Schild double copy in curved spacetime

The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

Alexander Ochirov

Niclas Westerberg

Perturbative spacetimes from Yang-Mills theory

Advances in our understanding of perturbation theory suggest the existence of a correspondence between classical general relativity and Yang-Mills theory. A concrete example of this correspondence, which is known as the double copy, was recently intro-duced for the case of stationary Kerr-Schild spacetimes. Building on this foundation, we examine the simple time-dependent case of an accelerating, radiating point source. The gravitational solution, which generalises the Schwarzschild solution, includes a non-trivial stress-energy tensor. This stress-energy tensor corresponds to a gauge theoretic current in the double copy. We interpret both of these sources as representing the radiative part of the field. Furthermore, in the simple example of Bremsstrahlung, we determine a scattering amplitude describing the radiation, maintaining the double copy throughout. Our results provide the strongest evidence yet that the classical double copy is directly related to the BCJ double copy for scattering amplitudes.