宇宙学常数为负的$\mathfrak{su}(N)$ EYM理论中拓扑多毛黑洞的存在性
On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant
摘要：
研究了具有负宇宙学常数的四维$\mathfrak{su}(N)$ EYM理论黑洞解的存在性.我们的分析不同于以往的作品，我们概括了某些非球对称时空的场方程。我们证明了任何整数$N$的非平凡解的存在性，与$N-1$规范自由度。具体地说，我们证明了两个结果：固定值的初始参数和作为$|Λ|\rightarrow\infty$的解决方案的存在性，和存在的解决方案的任何$Λ<0$在现有的平凡的解决方案的某些邻域。在这两种情况下，我们都可以证明“无节点”解的存在，即所有规范场函数都没有零点;这一事实很有趣，因为我们预计其中一些可能是稳定的。
英文摘要：
We investigate the existence of black hole solutions of four dimensional $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. We prove the existence of non-trivial solutions for any integer $N$, with $N-1$ gauge degrees of freedom. Specifically, we prove two results: existence of solutions for fixed values of the initial parameters and as $|Λ|\rightarrow\infty$, and existence of solutions for any $Λ<0$ in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of `nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
