标题： 黑洞、复曲线和图论：修订卡斯纳的一个猜想 显示英文标题

标题： Black Holes, Complex Curves, and Graph Theory: Revising a Conjecture by Kasner

摘要： 比值$\sqrt{8/9}=2\sqrt{2}/3\approx 0.9428$和$\sqrt{3}/2 \approx 0.866$出现在黑洞物理的各种背景下，分别作为电荷与质量比$Q/M$或旋转参数$a/M$的值，用于 Reissner-Nordström 黑洞和 Kerr 黑洞。 在本工作中，在 Reissner-Nordström 情况下，我将这些比值与视界面积的量子化，或等价地与熵的量子化联系起来。 此外，这些比值还与 Kasner 一个世纪前的工作有关，他在其中推测某些来自复分析的序列可能具有量子解释。 这些数也出现在 Kerr 黑洞的情况下，但解释并不那么直接。 Kasner 比率也可能对于理解黑洞物理中的随机矩阵和随机图方法有相关性，例如通过与 Ramanujan 图相关的界限来理解量子信息的快速杂化。 有趣的是，一些其他复分析中的纯数学问题，特别是单位圆盘中的复插值，似乎与黑洞问题共享一些数学表达式，因此也涉及 Kasner 比率。 显示英文摘要

摘要： The ratios $\sqrt{8/9}=2\sqrt{2}/3\approx 0.9428$ and $\sqrt{3}/2 \approx 0.866$ appear in various contexts of black hole physics, as values of the charge-to-mass ratio $Q/M$ or the rotation parameter $a/M$ for Reissner-Nordstr\"om and Kerr black holes, respectively. In this work, in the Reissner-Nordstr\"om case, I relate these ratios with the quantization of the horizon area, or equivalently of the entropy. Furthermore, these ratios are related to a century-old work of Kasner, in which he conjectured that certain sequences arising from complex analysis may have a quantum interpretation. These numbers also appear in the case of Kerr black holes, but the explanation is not as straightforward. The Kasner ratio may also be relevant for understanding the random matrix and random graph approaches to black hole physics, such as fast scrambling of quantum information, via a bound related to Ramanujan graph. Intriguingly, some other pure mathematical problems in complex analysis, notably complex interpolation in the unit disk, appear to share some mathematical expressions with the black hole problem and thus also involve the Kasner ratio.