A double copy for N=2$$ \mathcal{N}=2 $$ supergravity: a linearised tale told on-shell

A bstractWe construct the on-shell double copy dictionary for linearised four-dimensional N=2$$ \mathcal{N}=2 $$ 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.