Kerr-Newman-de Sitter带电黑洞族的非线性稳定性
Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
摘要：
我们证明了全局非线性稳定性，没有对称性假设，缓慢旋转带电黑洞在德西特时空的背景下的初值问题的爱因斯坦-麦克斯韦方程组：如果扰动一个缓慢旋转的Kerr-Newman-de Sitter（KNdS）黑洞的初始数据，那么在黑洞外部区域的邻域中，对于KNdS族的可能不同的成员，度量和电磁场以指数方式快速衰减到它们的值。这是一个延续最近的工作，作者与Vasy的稳定性的Kerr-de Sitter家庭的爱因斯坦真空方程。我们的非线性迭代方案自动找到最终的黑洞参数以及在其中存在的整体解决方案的规范，我们工作在一个广义波坐标/洛伦兹规范，与规范源函数躺在一个合适的有限维空间。我们包括一个独立的证明的线性模式稳定的Reissner-Nordström-de Sitter黑洞，由Kodama-Ishibashi工作的基础上。在我们的非线性稳定性论证的过程中，我们还获得了第一个证明的线性（模式）稳定性的缓慢旋转KNdS黑洞使用鲁棒微扰技术。
英文摘要：
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a neighborhood of the exterior region of the black hole, the metric and the electromagnetic field decay exponentially fast to their values for a possibly different member of the KNdS family. This is a continuation of recent work of the author with Vasy on the stability of the Kerr-de Sitter family for the Einstein vacuum equations. Our non-linear iteration scheme automatically finds the final black hole parameters as well as the gauge in which the global solution exists; we work in a generalized wave coordinate/Lorenz gauge, with gauge source functions lying in a suitable finite-dimensional space. We include a self-contained proof of the linear mode stability of Reissner-Nordström-de Sitter black holes, building on work by Kodama-Ishibashi. In the course of our non-linear stability argument, we also obtain the first proof of the linear (mode) stability of slowly rotating KNdS black holes using robust perturbative techniques.
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