具有四次自相互作用的稳定彩色黑洞
Stable colored black holes with quartic self-interactions
AI总结：
本文通过解析方法证明了具有四次自相互作用的非阿贝尔黑洞的线性径向稳定性，研究了非阿贝尔磁荷控制的背景解，并探讨了不同分支的稳定性特性。
摘要：
我们通过解析方法证明了非阿贝尔四次自相互作用黑洞的线性径向稳定性。该背景解基于Wu-Yang磁单极子ansatz构造，是一个精确的黑洞解，具有由单一耦合参数χ控制的非阿贝尔磁荷Q_{NA}^2，并具有两个不同的分支。奇数分支始终稳定，而在偶数分支中，分支I的有效势为正，分支II的有效势为负，分别确立了稳定性与潜在不稳定性。分支II的潜在不稳定性与之与扰动不稳定的爱因斯坦-杨-米尔斯雷斯纳-诺尔斯特罗姆解的联系一致。分支I在整个物理域χ范围内保持线性稳定性，其中解是规则的且没有裸奇点。我们的结果证明了在四维中具有最小耦合非阿贝尔普劳卡自相互作用的首个线性稳定的渐近平坦 hairy 黑洞的存在。
英文摘要：
We analytically prove the linear radial stability of non-Abelian black holes with quartic self-interactions. The background, constructed from the Wu-Yang magnetic monopole ansatz, is an exact black-hole solution carrying a non-Abelian magnetic charge $Q_{\rm NA}^2$ controlled by a single coupling parameter $χ$, and admits two distinct branches. The odd sector is always stable, while in the even sector the effective potential is positive for branch~I and negative for branch~II, establishing stability and potential instability, respectively. The potential instability of branch~II is consistent with its connection to the perturbatively unstable Einstein-Yang-Mills Reissner-Nordström solution. Branch~I remains linearly stable throughout the physical domain of $χ$ where the solutions are regular and free of naked singularities. The stability of branch~I is further confirmed through a numerical computation of the quasinormal mode spectrum using Leaver's continued fraction method and time-domain evolution supplemented with Prony method, showing no unstable modes. Our results prove the existence of the first linearly stable asymptotically flat hairy black holes in four dimensions with a minimally coupled non-Abelian Proca self-interaction.
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