论文标题
固定真空黑洞的模量空间可集成性
Moduli space of stationary vacuum black holes from integrability
论文作者
论文摘要
我们考虑将四个和五个维度的渐近平坦，固定，真空黑洞的空间分类，分别接受一个和两个通勤轴向杀戮场。众所周知，爱因斯坦方程将二维轨道空间上的谐波图减少为谐波图，该轨道空间本身是光谱方程的线性系统的整合性条件。我们沿着轨道空间的边界整合了Belinski-Zakharov光谱方程，并使用它来完全确定轴和视野上的度量和相关的ERNST和扭曲电势。对于任何给定的杆结构，这足以得出轴上没有圆锥形奇异性的溶液的模量空间。作为这种方法的说明，我们为Kerr和Myers-Perry黑洞以及已知的双重旋转黑环获得了建设性的独特性证明。
We consider the classification of asymptotically flat, stationary, vacuum black hole spacetimes in four and five dimensions, that admit one and two commuting axial Killing fields respectively. It is well known that the Einstein equations reduce to a harmonic map on the two-dimensional orbit space, which itself arises as the integrability condition for a linear system of spectral equations. We integrate the Belinski-Zakharov spectral equations along the boundary of the orbit space and use this to fully determine the metric and associated Ernst and twist potentials on the axes and horizons. This is sufficient to derive the moduli space of solutions that are free of conical singularities on the axes, for any given rod structure. As an illustration of this method we obtain constructive uniqueness proofs for the Kerr and Myers-Perry black holes and the known doubly spinning black rings.
