论文标题
切片可还原的保形杀死张量，光子表面和阴影
Slice-reducible conformal Killing tensors, photon surfaces and shadows
论文作者
论文摘要
我们概括了我们最近的方法来构建第二级排名的杀戮张量以进行保形杀死张量。该方法旨在用于任意维度$ m $的叶面空间，这些尺寸有一组保形杀伤向量。它适用于比以前的文献更通用结构的叶面。一个基本思想是从可简化的杀伤量张量开始，该切片中的切片和诱导的指标构成，然后将它们提升到整个歧管。得出了确保这一点的集成性条件，并提出了建设性的提升过程。由此产生的保形杀伤量可能是不可约的。结果表明，如果满足一些其他光子区域不等式，则适合该方法的叶面切片的子域是基本的光子表面。因此，我们的过程还为获得引力阴影边界的简单一般分析表达开辟了道路。我们将此技术应用于电动汽车，以及$ {\ cal n} = 2，\，4，\，8 $超级黑洞，提供了一种新的简便方法，以确定精确和共形的杀伤量。
We generalize our recent method for constructing Killing tensors of the second rank to conformal Killing tensors. The method is intended for foliated spacetimes of arbitrary dimension $m$, which have a set of conformal Killing vectors. It applies to foliations of a more general structure than in previous literature. The basic idea is to start with reducible Killing tensors in slices constructed from a set of conformal Killing vectors and the induced metric, and then lift them to the whole manifold. Integrability conditions are derived that ensure this, and a constructive lifting procedure is presented. The resulting conformal Killing tensor may be irreducible. It is shown that subdomains of foliation slices suitable for the method are fundamental photon surfaces if some additional photon region inequality is satisfied. Thus our procedure also opens the way to obtain a simple general analytical expression for the boundary of the gravitational shadow. We apply this technique to electrovacuum, and ${\cal N}=2,\,4,\,8$ supergravity black holes, providing a new easy way to establish the existence of exact and conformal Killing tensors.
