标题： Kerr-AdS 扰动的边界条件 显示英文标题

标题： Boundary Conditions for Kerr-AdS Perturbations

摘要： Teukolsky主方程及其相关的自旋权重球谐函数分解极大地简化了对Kerr（-AdS）黑洞的线性引力扰动的研究。然而，在我们指定物理上相关的边界条件之前，问题的表述并不完整。我们发现一组两个必须施加在Teukolsky主变量上的Robin边界条件，以得到渐近全局AdS的扰动，即渐近于爱因斯坦静态宇宙的扰动。在AdS/CFT对应关系的背景下，这些边界条件允许CFT应力能量张量具有非零的期望值，同时固定边界度规。当旋转消失时，我们还找到了Teukolsky和Kodama-Ishibashi（Regge-Wheeler-Zerilli）形式主义之间的规范不变微分映射。其中一个Robin边界条件映射到Kodama-Ishibashi分解的标量部分，另一个映射到矢量部分。Teukolsky变量上的Robin边界条件将允许对Kerr-AdS黑洞的不稳定时间尺度和准正规模谱进行定量研究。作为这个项目的热身，我们使用Teukolsky形式主义来恢复全局AdS-Schwarzschild的准正规模谱，补充了文献中的先前分析。 显示英文摘要

摘要： The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.