  We give a novel formulation of classical double copy in the mini-superspace
of static, spherically symmetric black holes where the map between the
solutions of general relativity and Maxwell's theory can be realized in
Boyer-Lindsquit coordinates. By employing the reduced action principle, we show
that the double copy structure can be generalized to Lovelock gravities and
quasi-topological gravities. However, the gravitational solutions are mapped to
the purely electric solutions of Maxwell's theory with a difference: instead of
a direct match between the Kerr-Schild scalar in the gravity side and the
scalar potential in the gauge theory side, the scalar potential becomes a
polynomial in the Kerr-Schild scalar, giving rise to a generalization of the
Kerr-Schild double copy. We calculate the Regge-Teitelboim surface charges and
prove that the mass of the black hole solution is identified with the electric
charge corresponding to the Coulomb part of the gauge theory solution in the
same way it does in the case of general relativity.
