Asymptotic Weyl double copy

A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that holds asymptotically in cases where full solution is algebraically general, using rotating STU supergravity black holes as example. The provides clues regarding relation between symmetries follows from copy. Using C-metric example, we show a previous interpretation this gravity superrotation has single analogue relating appropriate Li\'enard-Wiechert potential large gauge transformation.