标题： 可约共形Killing张量、光子曲面和阴影 显示英文标题

标题： Slice-reducible conformal Killing tensors, photon surfaces and shadows

摘要： 我们将我们最近提出的构造二阶Killing张量的方法推广到共形Killing张量。 该方法适用于任意维度 $m$ 的叶状时空，这些时空具有一组共形Killing矢量。 它适用于比先前文献中更一般的叶状结构。 基本思想是从一组共形Killing矢量和诱导度规构造的切片出发，开始处理可约化Killing张量，然后将其提升到整个流形。 推导了保证此过程成立的可积性条件，并给出了构造性提升步骤。 得到的共形Killing张量可能是不可约的。 证明了如果满足某些额外的光子区域不等式，则适合该方法的叶状切片子域是基本光子曲面。 因此，我们的程序也为获得引力阴影边界的简单一般解析表达式开辟了道路。 我们将此技术应用于电真空和 ${\cal N}=2,\,4,\,8$ 超重力黑洞，提供了一种新的简便方法来确定精确和共形Killing张量的存在性。 显示英文摘要

摘要： 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.