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arXiv 1208.3589gr-qchep-th
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Einstein-Yang-Mills理论中双子和双子黑洞的存在性

On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory

Brien C. Nolan, Elizabeth Winstanley

摘要:

研究了渐近反德西特空间中${\mathfrak {su}}(2)$ Einstein-Yang-Mills方程的双子孤子解和黑洞解.我们证明了在平凡解的邻域内存在非平凡的双子孤子和黑洞解。对于这些解决方案的磁规范场功能没有零,我们推测,至少有一些这些非平凡的解决方案将是稳定的。全局存在性证明使用局部存在性结果和基于(Banach空间)隐函数定理的非线性扰动参数。

英文摘要:

We study dyonic soliton and black hole solutions of the ${\mathfrak {su}}(2)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.

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