Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics
High Energy Physics - Theory
2008-11-26 v2 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.0705.4471,
title = {Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics},
author = {W. Chen and H. Lu},
journal= {arXiv preprint arXiv:0705.4471},
year = {2008}
}