黑洞、复曲线和图论:修正卡斯纳的猜想

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS
Yen Chin Ong
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引用次数: 0

摘要

8/9=22/3≈0.9428和3/2≈0.866这两个比值出现在黑洞物理学的不同语境中,分别作为赖斯纳-诺德斯特伦黑洞和克尔黑洞的电荷质量比Q/M或旋转参数a/M的值。在这项工作中,在赖斯纳-诺德斯特伦情况下,我将这些比率与视界面积的量子化或熵的量子化联系起来。此外,这些比率还与卡斯纳的一项百年前的研究有关,在这项研究中,他猜想复杂分析中产生的某些序列可能具有量子解释。这些数字也出现在克尔黑洞的情况中,但解释并不那么直接。卡斯纳比率也可能与理解黑洞物理学的随机矩阵和随机图方法有关,例如通过与拉马努扬图相关的约束来快速扰乱量子信息。有趣的是,复杂分析中的其他一些纯数学问题,特别是单位盘中的复杂插值,似乎与黑洞问题共享一些数学表达式,因此也涉及卡斯纳比率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Black holes, complex curves, and graph theory: Revising a conjecture by Kasner
The ratios 8/9=22/30.9428 and 3/20.866 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-Nordström and Kerr black holes, respectively. In this work, in the Reissner-Nordström 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.
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来源期刊
Nuclear Physics B
Nuclear Physics B 物理-物理:粒子与场物理
CiteScore
5.50
自引率
7.10%
发文量
302
审稿时长
1 months
期刊介绍: Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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