论文标题
kerr的保守电流和准模式的正交性
Conserved currents for Kerr and orthogonality of quasinormal modes
论文作者
论文摘要
我们引入了Kerr的Weyl标量扰动的双线性形式。该形式是对称和保守的,我们表明,当与涉及复杂的R整合轮廓的合适的重新归一化处方结合时,准模式在双线性形式的正交形式是正交的(L,M,M,N)。这些属性显然是标准特性对径向和角度解的影响,对脱钩的Teukolsky关系,并且依赖于Kerr的Petrov D型特征及其t- $ ϕ $反射等轴测图。我们表明,准模式激发系数是通过相对于我们的双线性形式的投影确切给出的。这些属性可以使我们的双线性形式有助于在Kerr中建立非线性准模式耦合的框架。我们还提供了有关保守的本地电流及其相关的局部对称性操作员的一般讨论,以进行度量和WEYL扰动,并识别包含越来越多的衍生物的集合。
We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form is symmetric and conserved, and we show that, when combined with a suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the bilinear form for different (l, m, n). These properties are apparently not evident consequences of standard properties for the radial and angular solutions to the decoupled Teukolsky relations and rely on the Petrov type D character of Kerr and its t-$ϕ$ reflection isometry. We show that quasinormal mode excitation coefficients are given precisely by the projection with respect to our bilinear form. These properties can make our bilinear form useful to set up a framework for nonlinear quasinormal mode coupling in Kerr. We also provide a general discussion on conserved local currents and their associated local symmetry operators for metric and Weyl perturbations, identifying a collection containing an increasing number of derivatives.