At least in some form this “Gibbons–Hawking approximation” of hyperkähler metrics on the K3 surface seems to be known to physicists in the context of the duality between M theory compactified on the K3 surface and Type IIA String theory compactified on $T^{3}/\mathbb{Z}_{2}$. For example, in [38] Sen discusses the physical interpretation of dihedral ALF spaces thought of as a “superposition” of Taub–NUT spaces and the Atiyah–Hitchin manifold, cf. Remark 3.7.