Kerr–Schild structure and harmonic 2-forms on (A)dS–Kerr–NUT metrics
Kerr–Schild structure and harmonic 2-forms on (A)dS–Kerr–NUT metrics
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DOI：
10.1016/j.physletb.2007.09.066
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发表时间：
2007-05
影响因子：
4.4
通讯作者：
W. Chen;Hong Lu
中科院分区：
文献类型：
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作者：
W. Chen;Hong Lu
证明了具有（[D/2]，[（D+1）/2]）特征的D维广义（A）dS-Kerr-NUT解存在[D/2]线性无关，相互正交和仿射参数化的零测地同余.这使我们能够以多克尔-希尔德形式编写度量，其中质量和所有NUT参数线性地进入度量。在D=2n的情况下，我们还得到了n个高维Einstein-Maxwell理论的2-形式，它可以看作是小电荷展开的线性水平上的带电（A）dS-Kerr-NUT解.在BPS极限下，这些2-形式简化为n−1个线性无关的形式，而由此产生的卡-丘度量获得了凯勒2-形式，总数保持不变。
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 Kähler 2-form, leaving the total number the same.