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arXiv 1609.09427hep-thgr-qc
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具有非线性磁单极子的四维极端旋转正则黑洞中的Kerr/CFT对应

Kerr/CFT correspondence in a 4D extremal rotating regular black hole with a non-linear magnetic monopole

Shingo Takeuchi

备注：
23 pages; v5: accepted version
发表信息：
Nucl.Phys.B921 (2017) 375-393
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AI总结：

本文研究具有非线性磁单极子的四维极端旋转正则黑洞中的Kerr/CFT对应，通过将正则化效应作微扰处理克服视界方程困难，得到修正的NHEK几何并验证Cardy熵与Bekenstein-Hawking熵一致。

摘要：

我们在一个具有非线性磁单极子（NLMM）的四维极端旋转正则黑洞中开展Kerr/CFT对应研究。本研究中的一个问题是：我们的几何是否能成为一个解。基于带有NLMM的Schwarzschild正则黑洞几何可以是一个解这一事实，我们寻找使我们的旋转几何成为解的方法。然而，在尝试对我们自然可以考虑的Schwarzschild情形进行推广时，结果表明不可能构造一个使我们的几何成为精确解的模型。我们利用我们的几何在除黑洞核心区域外的整个时空中可以近似成为解这一事实来处理该问题。作为下一个问题，由于正则化效应，求视界半径的方程被证明由一个五阶方程给出。我们通过将正则化效应作微扰处理来克服这一问题。结果，我们能够得到带有正则化效应修正的近视界极端Kerr（NHEK）几何。一旦得到NHEK几何，我们就可以得到对偶CFT中的中心荷和Frolov-Thorne温度。利用这些量，我们通过Cardy公式计算其熵，该结果与由Bekenstein-Hawking熵计算得到的结果一致。

英文摘要：

We carry out the Kerr/CFT correspondence in a four-dimensional extremal rotating regular black hole with a non-linear magnetic monopole (NLMM). One problem in this study would be whether our geometry can be a solution or not. We search for the way making our rotating geometry into a solution based on the fact that the Schwarzschild regular black hole geometry with a NLMM can be a solution. However, in the attempt to extend the Schwarzschild case that we can naturally consider, it turns out that it is impossible to construct a model in which our geometry can be a exact solution. We manage this problem by making use of the fact that our geometry can be a solution approximately in the whole space-time except for the black hole's core region. As a next problem, it turns out that the equation to obtain the horizon radii is given by a fifth-order equation due to the regularization effect. We overcome this problem by treating the regularization effect perturbatively. As a result, we can obtain the near-horizon extremal Kerr (NHEK) geometry with the correction of the regularization effect. Once obtaining the NHEK geometry, we can obtain the central charge and the Frolov-Thorne temperature in the dual CFT. Using these, we compute its entropy through the Cardy formula, which agrees with the one computed from the Bekenstein-Hawking entropy.

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