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Register a new userClassical double copy at null infinity
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We give two double copy prescriptions which construct asymptotically flat solutions in gravity from asymptotically flat gauge fields. The first prescription applies to radiative fields, which are non-linear vacuum solutions determined by characteristic data at null infinity. For any two such radiative gauge fields (linear or non-linear), the characteristic data of a radiative metric, dilaton and axion is constructed by a simple `squaring procedure, giving a classical double copy at the level of radiation fields. We demonstrate the procedure with several examples where the characteristic data can be explicitly integrated; for linear fields this also sheds light on the twistorial description of Weyl double copy. Our second prescription applies to all asymptotically flat fields at the level of their asymptotic equations of motion: we give a map between any solution of the asymptotic Maxwell equations and any solution of the asymptotic Einstein equations at null infinity. This also extends to the asymptotic charges and their duals, preserves the soft and hard sectors between gauge theory and gravity, and is related to the usual notion of double copy in scattering amplitudes.
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We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits. As an application, we reproduce the leading post-Newtonian radiation fields and energy flux for point masses in non-relativistic orbits from the double copy of gauge theory.
The area of a cross-sectional cut $Sigma$ of future null infinity ($mathcal{I}^+$) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The renormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of $mathcal{I}^+$ to the future of $Sigma$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $Sigma$. In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across $Sigma$ of the outgoing quantum state on $mathcal{I}^+$.
We extend Shens recent formulation (arXiv:1806.07388) of the classical double copy, based on explicit color-kinematic duality, to the case of finite-size sources with non-zero spin. For the case of spinning Yang-Mills sources, the most general consistent double copy consists of gravitating objects which carry pairs of spin degrees of freedom. We find that the couplings of such objects to background fields match those of a classical (i.e. heavy) closed bosonic string, suggesting a string theory interpretation of sources related by color-kinematics duality. As a special case, we identify a limit, corresponding to unoriented strings, in which the 2-form Kalb-Ramond axion field decouples from the gravitational side of the double copy. Finally, we apply the classical double copy to extended objects, described by the addition of finite-size operators to the worldline effective theory. We find that consistency of the color-to-kinematics map requires that the Wilson coefficients of tidal operators obey certain relations, indicating that the extended gravitating objects generated by the double copy of Yang-Mills are not completely generic.
We establish a correspondence between perturbative classical gluon and gravitational radiation emitted by spinning sources, to linear order in spin. This is an extension of the non-spinning classical perturbative double copy and uses the same color-to-kinematic replacements. The gravitational theory has a scalar (dilaton) and a 2-form field (the Kalb-Ramon axion) in addition to the graviton. In arXiv:1712.09250, we computed axion radiation in the gravitational theory to show that the correspondence fixes its action. Here, we present complete details of the gravitational computation. In particular, we also calculate the graviton and dilaton amplitudes in this theory and find that they precisely match with the predictions of the double copy. This constitutes a non-trivial check of the classical double copy correspondence, and brings us closer to the goal of simplifying the calculation of gravitational wave observables for astrophysically relevant sources.
We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) $phi$ and the Kalb-Ramond axion field $B_{mu u}$. Consistency of the double copy imposes constraints on the parameters of the theory on both the gauge and gravity sides of the correspondence. In particular, the color charges carry a chromomagnetic interaction which, in $d=4$, corresponds to a gyromagnetic ratio equal to Diracs value $g=2$. The color-to-kinematics map implies that on the gravity side, the bulk theory of the fields $(phi,g_{mu u},B_{mu u})$ has interactions which match those of $d$-dimensional `string gravity, as is the case both in the BCJ double copy of pure gauge theory scattering amplitudes and the KLT relations between the tree-level $S$-matrix elements of open and closed string theory.
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