A double copy for ${\cal N}=2$ supergravity: a linearised tale told   on-shell
  We construct the on-shell double copy for linearised four-dimensional ${\cal N}=2$ supergravity coupled to one vector multiplet with a quadratic prepotential. We apply this dictionary to the weak-field approximation of dyonic BPS black holes in this theory. 
G.L.Cardoso, S.Nagy and Suresh Nampuri
hep-th