Geometric Microstates for the Three Dimensional Black Hole
Geometric Microstates for the Three Dimensional Black Hole
复制标题
三维黑洞的几何微观状态
DOI：
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发表时间：
2015
期刊：
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通讯作者：
A. Maloney
中科院分区：
文献类型：
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作者：
A. Maloney
本文研究了三维黑洞的微观态，这些微观态是通过对视界后的拓扑非平凡几何进行量子化而得到的。在手征引力中，这些状态是通过量子化加边黎曼曲面的模空间而得到的。在半经典极限下，这些微观态可以在穿孔黎曼曲面的模空间上用相交理论计数。我们做一个猜想（支持数值）的渐近行为的相关交叉数。结果是，具有固定拓扑结构的几何微观态的熵增长太慢，无法解释半经典的贝肯斯坦-霍金熵。然而，拓扑上的求和会导致发散。最后，我们对如何解决这一问题以给出与视界面积成正比的熵进行了一些推测。
We study microstates of the three dimensional black hole obtained by quantizing topologically non-trivial geometries behind the event horizon. In chiral gravity these states are found by quantizing the moduli space of bordered Riemann surfaces. In the semi-classical limit these microstates can be counted using intersection theory on the moduli space of punctured Riemann surfaces. We make a conjecture (supported by numerics) for the asymptotic behaviour of the relevant intersection numbers. The result is that the geometric microstates with fixed topology have an entropy which grows too slowly to account for the semiclassical Bekenstein-Hawking entropy. The sum over topologies, however, leads to a divergence. We conclude with some speculations about how this might be resolved to give an entropy proportional to horizon area.