标题： 爱因斯坦-杨-Mills sphalerons 和黑洞周围的负模态 显示英文标题

标题： Negative modes around Einstein-Yang-Mills sphalerons and black holes

摘要： 在规范群$SU(2)$的爱因斯坦-杨-Mills 理论中，研究了围绕 sphaleron 和黑洞解的小扰动的动力学。 扰动可以根据其奇偶性分成两个独立的分支；每个分支都包含负模式。 偶奇性负模式被证明对应于 sphaleron 附近势能屏障高度的负二阶变分。 对于奇奇性分支，严格证明了恰好存在$n$个（sphaleron 解的规范场函数的节点数）负模式。 同样的结果也适用于爱因斯坦-杨-Mills 黑洞。 显示英文摘要

摘要： The dynamics of small perturbations around sphaleron and black hole solutions in the Einstein-Yang-Mills theory for the gauge group $SU(2)$ is investigated. The perturbations can be split into the two independent sectors in accordance with their parity; each sector contains negative modes. The even-parity negative modes are shown to correspond to the negative second variations of the height of the potential energy barrier near the sphaleron. For the odd-parity sector, the existence of precisely $n$ (the number of nodes of the sphaleron solution gauge field function) negative modes is rigorously proven. The same results hold for the Einstein-Yang-Mills black holes as well.