论文标题
在koutras-mcintosh空位中杀死张量
Killing Tensors in Koutras-McIntosh Spacetimes
论文作者
论文摘要
Koutras-McIntosh指标家族包括保态扁平的PP波和Wils Metric。它出现在1996年的库特拉斯·麦金托什（Koutras-McIntosh）的论文中，作为无标量曲率不变的纯辐射时空或无限对称性的一个例子。在这里，我们证明这些指标没有“隐藏对称性”，这是指杀死低度的张量。对于WILS指标的特殊情况，我们表明将张力张量杀死6级的不存在。 我们使用的技术是过度确定的PDE的几何理论和Cartan延长预测方法。这些应用程序可以证明多项式在Momenta积分中的不存在，以数学上的严格方式对地球化学方程式证明。使用相同的技术，我们可以完全对所有低度杀死张量进行分类，尤其是证明，对于通用PP波，所有杀死3和4的杀伤量都是可降低的。
The Koutras-McIntosh family of metrics include conformally flat pp-waves and the Wils metric. It appeared in a paper of 1996 by Koutras-McIntosh as an example of a pure radiation spacetime without scalar curvature invariants or infinitesimal symmetries. Here we demonstrate that these metrics have no "hidden symmetries", by which we mean Killing tensors of low degrees. For the particular case of Wils metrics we show the nonexistence of Killing tensors up to degree 6. The technique we use is the geometric theory of overdetermined PDEs and the Cartan prolongation-projection method. Application of those allows to prove the nonexistence of polynomial in momenta integrals for the equation of geodesics in a mathematical rigorous way. Using the same technique we can completely classify all lower degree Killing tensors and, in particular, prove that for generic pp-waves all Killing tensors of degree 3 and 4 are reducible.
