Kerr–Schild structure and harmonic 2-forms on (A)dS–Kerr–NUT metrics

We demonstrate that the general (A)dS–Kerr–NUT solutions in D   dimensions with ([D/2],[(D+1)/2])([D/2],[(D+1)/2]) signature admit [D/2][D/2] linearly-independent, mutually-orthogonal and affinely-parameterised null geodesic congruences. This enables us to write the metrics in a multi-Kerr–Schild form, where the mass and all of the NUT parameters enter the metrics linearly. In the case of D=2nD=2n, we also obtain n   harmonic 2-forms, which can be viewed as charged (A)dS–Kerr–NUT solution at the linear level of small-charge expansion, for the higher-dimensional Einstein–Maxwell theories. In the BPS limit, these 2-forms reduce to n−1n−1 linearly-independent ones, whilst the resulting Calabi–Yau metric acquires a Kähler 2-form, leaving the total number the same.