The Hesse potential, the c-map and black hole solutions
The Hesse potential, the c-map and black hole solutions
复制标题
黑塞势、c 图和黑洞解
DOI：
10.1007/jhep07(2012)163
复制
发表时间：
2011
影响因子：
5.4
通讯作者：
O. Vaughan
中科院分区：
文献类型：
--
作者：
T. Mohaupt;O. Vaughan
本文利用特殊Kähler几何的辛协变真实的形式，给出了局部c-映射的一个新形式.我们得到了四元数Kähler度规的一个显式的简单表达式，或者，在随时间约化的情况下，用黑森势表示的仿四元数Kähler度规的一个显式的简单表达式，它类似于从刚性r-和c-映射得到的度规的表达式，作为一个应用，我们使用的c-的时态版本，映射从标量流形的几何性质导出黑洞吸引子方程，而不施加超对称或球对称。我们观察到，一般（非对称）的c-映射空间的静态BPS解决方案有关的一个典型的家庭完全迷向，全测地子流形。静态非BPS解决方案可以通过应用一个非平凡的兼容性条件下的场旋转矩阵。我们表明，一类prepotential，其中包括非常特殊的（“立方”）prepotential作为一个子类，无轴的解决方案总是承认一个非平凡的字段旋转矩阵。
A bstractWe present a new formulation of the local c-map, which makes use of a symplectically covariant real formulation of special Kähler geometry. We obtain an explicit and simple expression for the resulting quaternionic, or, in the case of reduction over time, para-quaternionic Kähler metric in terms of the Hesse potential, which is similar to the expressions for the metrics obtained from the rigid r- and c-map, and from the local r-map.As an application we use the temporal version of the c-map to derive the black hole attractor equations from geometric properties of the scalar manifold, without imposing supersymmetry or spherical symmetry. We observe that for general (non-symmetric) c-map spaces static BPS solutions are related to a canonical family of totally isotropic, totally geodesic submanifolds. Static non-BPS solutions can be obtained by applying a field rotation matrix which is subject to a non-trivial compatibility condition. We show that for a class of prepotentials, which includes the very special (‘cubic’) prepotentials as a subclass, axion-free solutions always admit a non-trivial field rotation matrix.