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It is well-known that General Relativity (GR) in three spacetime dimensions (3D) has no well-defined Newtonian limit. Recently, a static solution mimicking the behaviour of the expected Newtonian potential has been found in arXiv:1904.11001 by studying the classical double copy of a point charge in gauge theory. This is the first example where the vacuum solution in the gauge theory leads to a non-vacuum solution on the gravity side. The resulting energy-momentum tensor was attributed to a free scalar ghost field; however, alternatively, the source can be seen as one resulting from a spacelike perfect fluid. In this paper, we first give an alternative derivation of the solution where there is no need to perform a generalized gauge transformation to obtain a quadratic Lagrangian without propagating ghost fields. Then, we present a stationary version of the solution and show that the scalar field interpretation of the source does not survive in this case, leaving the spacelike fluid as the only possibility. We give the gauge theory single copy of our solution and comment on the implications of our results on the validity of the classical double copy in 3D. The effect of the cosmological constant is also discussed.
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Recent explorations on how to construct a double copy of massive gauge fields have shown that, while any amplitude can be written in a form consistent with colour-kinematics duality, the double copy is generically unphysical. In this paper, we explore a new direction in which we can obtain a sensible double copy of massive gauge fields due to the special kinematics in three-dimensional spacetimes. To avoid the appearance of spurious poles at 5-points, we only require that the scattering amplitudes satisfy one BCJ relation. We show that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy at three, four, and five-points is Topologically Massive Gravity.
While the Kerr-Schild double copy of the Coulomb solution in dimensions higher than three is the Schwarzschild black hole, it is known that it should be a non-vacuum solution in three dimensions. We show that the static black hole solution of Einstein-Maxwell theory (with one ghost sign in the action) is the double copy with the correct Newtonian limit, which provides an improvement over the previous construction with a free scalar field that does not vanish at infinity. By considering a negative cosmological constant, we also study the charged Ba~nados-Teitelboim-Zanelli black hole and find that the single copy gauge field is the Coulomb solution modified by a term which describes an electric field linearly increasing with the radial coordinate, which is the usual behaviour of the Schwarzschild-AdS black hole in higher dimensions when written around a flat background metric.
The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwells theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.
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.
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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