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arXiv · 0705.4471

Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics

W. Chen·H. Lu
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Abstract

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.

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W. Chen, H. Lu. 2007-06-19. Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics. https://doi.org/10.1016/j.physletb.2007.09.066

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