Exact classical double copy for generic vacuum spacetimes
In plain words
Some exact black-hole solutions of Einstein's equations are squares of simple electromagnetic solutions. Whether every solution of Einstein's equations has such a gauge-theory partner is unknown.
Precise statement
The Kerr-Schild double copy (2014), the Weyl double copy (2018) and the self-dual double copy (Monteiro and O'Connell, 2011) map Kerr-Schild, algebraically special (Petrov types D and N) and self-dual vacuum metrics to exact Maxwell or Yang-Mills solutions. Determine whether an exact, nonperturbative map exists from every Ricci-flat 4D metric, including Petrov type I, to solutions of gauge-theory field equations that reduces to the amplitude double copy order by order, or prove that none exists.
What would settle it
A constructive map valid for Petrov type I spacetimes with a proof of its perturbative agreement, or a no-go theorem.
Status in the literature
Unverified note
Exact maps exist for Kerr-Schild metrics, for Petrov type D and N vacuum solutions (Weyl double copy) and for self-dual solutions; no exact map for Petrov type I is known as of 2026.