极值黑洞与幂零轨道
Extremal black holes and nilpotent orbits
摘要：
各种各样的（超）引力理论的定态解都可以用一个耦合到三维欧氏引力的非线性西格玛模型G / H* 来描述，其中G是一个单群，H* 是它的极大紧子群的非紧实形式。在四维空间中不存在裸奇点，这就要求三维空间中的G Noether电荷满足一个特征方程，该方程决定了它是溶液的质量、NUT电荷和电磁电荷的函数。由此得出，与极值黑洞有关的Noether荷必定位于G的幂零轨道的某个拉格朗日子流形中。构建一个合适的参数化的拉格朗日，我们能够确定所谓的“假超势”，管理径向依赖的标量场。
英文摘要：
The stationary solutions of a large variety of (super)gravity theories can be described within a non-linear sigma model G / H* coupled to Euclidean gravity in three-dimensions, for which G is a simple group and H* a non-compact real form of its maximal compact subgroup. The absence of naked singularities in four dimensions requires the G Noether charge in 3D to satisfy a characteristic equation that determines it in function of the mass, the NUT charge and the electro-magnetic charges of the solution. It follows that the Noether charge associated to extremal black holes must lie in a certain Lagrangian submanifold of a nilpotent orbit of G. Constructing a suitable parameterisation of this Lagrangian, we are able to determine the so-called `fake superpotential' that governs the radial dependency of the scalar fields.
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