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]) signature admit [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 = 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 - 1 linearly-independent ones, whilst the resulting Calabi-Yau metric acquires a Kahler 2-form, leaving the total number the same. Published by Elsevier B.V.