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arXiv 1104.2830hep-thgr-qc
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D=2n+1维的Einstein-Yang-Mills-Chern-Simons解

Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

Yves Brihaye, Eugen Radu, D. H. Tchrakian

备注：
34 pages, 14 figures; v2: misprints corrected and references added
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摘要：

本文研究了奇数维时空中Einstein-Yang-Mills-Chern-Simons系统的有限能量解，D=2n+1，其中n>1.我们的组态是静态的和球对称的，在无穷远处接近闵可夫斯基时空背景。与阿贝尔情形相反，陈-西蒙斯项的贡献在静态球对称极限中已经是非平凡的了。对于不同的D值，我们用数值方法构造了全局正则的类粒子解和黑洞。这些溶液带有非零电荷，质量有限。对于整体正则解，电荷的值由Chern-Simons耦合常数确定。黑洞可以被认为是Reissner-Nordstrom和非阿贝尔组态的非线性叠加。系统地讨论了D=5时的解，在这种情况下，Reissner-Nordstrom黑洞变得不稳定，并发展出非阿贝尔头发。我们发现，这些非阿贝尔配置下的线性，球对称扰动是稳定的。一个精确的D=5的解决方案描述极端黑洞和孤子的详细讨论也提供。

英文摘要：

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1, with n>1. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particle-like solutions and black holes are constructed numerically for several values of D. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought as non-linear superpositions of Reissner-Nordstrom and non-Abelian configurations. A systematic discussion of the solutions is given for D=5, in which case the Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact D=5 solution describing extremal black holes and solitons is also provided.

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