揭开第一个非线性带电旋转黑洞的电动力学
Unveiling the electrodynamics of the first nonlinearly charged rotating black hole
摘要：
经过多年的努力，Garcia-Diaz在最近的两项工作中终于报道了第一个非线性带电旋转黑洞。这是广义相对论中悬而未决的一个重要结果，因为当时还不知道克尔-纽曼解的非线性推广。不幸的是，支持这种配置的拉格朗日不能用初等函数的标准不变量来表示。在目前的工作中，我们绕过这个问题，使用非线性电动力学的混合电磁本征值，介绍了萨拉查，加西亚-迪亚兹和普莱班斯基近四十年前的配方。在这样做的时候，我们证明，基本的理论成为完全确定的，因此新发现的非线性带电静止轴对称时空对应于一个定义良好的自引力非线性电动力学的精确解，其基本结构函数在这里提供。
英文摘要：
After many years of efforts, the first nonlinearly charged rotating black hole has been finally reported by Garcia-Diaz in two recent works. This is an important result that was pending in General Relativity, since nonlinear generalizations of the Kerr-Newman solution were not yet known. Unfortunately, the Lagrangian supporting this configuration cannot be expressible in terms of the standard invariants using elementary functions. In the present work we circumvent this problem by using the formulations of nonlinear electrodynamics in terms of mixed electromagnetic eigenvalues, introduced by Salazar, Garcia-Diaz and Plebanski almost four decades ago. In doing so, we prove that the underlying theory becomes fully determined, and hence the new found nonlinearly charged stationary axisymmetric spacetimes correspond to exact solutions of a well-defined self-gravitating nonlinear electrodynamics whose fundamental structural functions are provided here.
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