Closed conformal Killing–Yano initial data

Abstract

Through an exhaustive search, we produce a five-parameter family of propagation identities for the closed conformal Killing–Yano (cCYK) equation on two-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension n > 4. It is well-known that spacetimes admitting a non-degenerate two-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein’s field equations admits a cCYK two-form. We refer to these conditions as closed conformal Killing–Yano initial data equations. The four-dimensional case is special and is treated separately, where we can also handle the conformal Killing–Yano equation without the closed condition.