Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes
Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes
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广义波算子、加权杀伤场和高维时空扰动
DOI：
10.1088/1361-6382/aab06a
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发表时间：
2017
影响因子：
3.5
通讯作者：
Bernardo Araneda
中科院分区：
文献类型：
--
作者：
Bernardo Araneda
我们给出了任意维的某些代数特殊爱因斯坦时空的扰动的加权协变导数和波动算子，在这些扰动下，Teukolsky方程和相关方程成为加权波动方程。我们证明了主零方向的高维推广是关于修正协变导数的加权保形杀伤向量。我们还引入了一个作用于张量值微分形式的改进的类拉普拉斯算子，并证明了类波方程在线性水平上是作用于曲率张量的算子的适当的壳投影；投影张量是由加权共形kill - yano张量构成的。我们给出了壳算子恒等式，将爱因斯坦方程和麦克斯韦方程映射为加权标量方程，并利用伴随算子从类波方程的解构造出紧致形式的原场方程的解。研究了极值和零升力情况；与昆特时空扰动（包括极端黑洞的近视界几何）对应的极端增压，以及对任意维度的静态黑洞的零增压。在4D中，我们的结果应用于D型Petrov的爱因斯坦时空，并利用了加权的kill旋量。
We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.
克尔时空中线性化引力的新恒等式
影响因子：
5
作者：
Aksteiner S
通讯作者：
Aksteiner S