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.

中文翻译：

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零无穷处的经典双副本

我们给出了两个双副本处方，它们从渐近平坦的规范场构造引力的渐近平坦解。第一个处方适用于辐射场，它是由零无穷处的特征数据确定的非线性真空解。对于任何两个这样的辐射规范场（线性或非线性），辐射度量、膨胀子和轴子的特征数据是通过简单的“平方”程序构建的，在辐射场水平上给出经典的双副本。我们通过几个示例来演示该过程，其中可以显式集成特征数据；对于线性场，这也阐明了 Weyl 双拷贝的扭曲描述。我们的第二个处方适用于所有在其渐近运动方程水平上的渐近平坦场：我们给出渐近麦克斯韦方程的任意解和渐近爱因斯坦方程在零无穷处的任意解之间的映射。这也扩展到渐近电荷及其对偶，保留了规范理论和引力之间的软硬部分，并且与散射振幅中双副本的通常概念有关。