Tomimatsu-Sato几何、全息术和量子引力
Tomimatsu-Sato geometries, holography and quantum gravity
摘要：
我们分析了$δ=2$ Tomimatsu-Sato时空的背景下，建议克尔/CFT对应。这个4维真空时空是渐近平坦的，有一个定义明确的ADM质量和角动量，但也涉及到几个奇异的特征，包括一个裸环奇点，和两个不相交的Killing视界，它们被一个封闭的类时曲线和一个棒状圆锥奇点分开。我们证明了近地平线几何属于一般类的Ricci平坦度规与$SL(2,\mathbb{R})\times U(1)$对称性，包括极值克尔和极值克尔螺栓几何。我们计算了这个时空的CFT对偶的中心荷和温度，并证实了Cardy公式再现了Bekenstein-Hawking熵。我们发现，所有的基本参数的双重CFT是最自然的表示在地平线上，这是不同于ADM收费在这个几何定义的收费。
英文摘要：
We analyze the $δ=2$ Tomimatsu-Sato spacetime in the context of the proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is asymptotically flat and has a well-defined ADM mass and angular momentum, but also involves several exotic features including a naked ring singularity, and two disjoint Killing horizons separated by a region with closed timelike curves and a rod-like conical singularity. We demonstrate that the near horizon geometry belongs to a general class of Ricci-flat metrics with $SL(2,\mathbb{R})\times U(1)$ symmetry that includes both the extremal Kerr and extremal Kerr-bolt geometries. We calculate the central charge and temperature for the CFT dual to this spacetime and confirm the Cardy formula reproduces the Bekenstein-Hawking entropy. We find that all of the basic parameters of the dual CFT are most naturally expressed in terms of charges defined intrinsically on the horizon, which are distinct from the ADM charges in this geometry.
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