Abstract
Double Kerr–Schild equivalence of hyperheavens is studied within a spinorial formalism based on the fact of the existence of a congruence of self-dual null strings. In particular, it is shown that a given hyperheavenly metric structure generates all members of the corresponding equivalence class in terms of a certain spinor field and the generalized key function subject to the generalized hyperheavenly equation. The treatment is manifestly covariant: no coordinates are employed. Finally, a link with the classical results on hyperheavens (Plebański and Robinson [J. F. Plebański and I. Robinson, Phys. Rev. Lett. 37, 493 (1976)] and Finley and Plebański [J. D. Finley, III and J. F. Plebański, J. Math. Phys. 17, 2207 (1976)]) is established.
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