黑洞、复杂曲线和图论:修正卡斯纳的猜想

Yen Chin Ong
{"title":"黑洞、复杂曲线和图论:修正卡斯纳的猜想","authors":"Yen Chin Ong","doi":"arxiv-2409.08236","DOIUrl":null,"url":null,"abstract":"The ratios $\\sqrt{8/9}=2\\sqrt{2}/3\\approx 0.9428$ and $\\sqrt{3}/2 \\approx\n0.866$ appear in various contexts of black hole physics, as values of the\ncharge-to-mass ratio $Q/M$ or the rotation parameter $a/M$ for\nReissner-Nordstr\\\"om and Kerr black holes, respectively. In this work, in the\nReissner-Nordstr\\\"om case, I relate these ratios with the quantization of the\nhorizon area, or equivalently of the entropy. Furthermore, these ratios are\nrelated to a century-old work of Kasner, in which he conjectured that certain\nsequences arising from complex analysis may have a quantum interpretation.\nThese numbers also appear in the case of Kerr black holes, but the explanation\nis not as straightforward. The Kasner ratio may also be relevant for\nunderstanding the random matrix and random graph approaches to black hole\nphysics, such as fast scrambling of quantum information, via a bound related to\nRamanujan graph. Intriguingly, some other pure mathematical problems in complex\nanalysis, notably complex interpolation in the unit disk, appear to share some\nmathematical expressions with the black hole problem and thus also involve the\nKasner ratio.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Black Holes, Complex Curves, and Graph Theory: Revising a Conjecture by Kasner\",\"authors\":\"Yen Chin Ong\",\"doi\":\"arxiv-2409.08236\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The ratios $\\\\sqrt{8/9}=2\\\\sqrt{2}/3\\\\approx 0.9428$ and $\\\\sqrt{3}/2 \\\\approx\\n0.866$ appear in various contexts of black hole physics, as values of the\\ncharge-to-mass ratio $Q/M$ or the rotation parameter $a/M$ for\\nReissner-Nordstr\\\\\\\"om and Kerr black holes, respectively. In this work, in the\\nReissner-Nordstr\\\\\\\"om case, I relate these ratios with the quantization of the\\nhorizon area, or equivalently of the entropy. Furthermore, these ratios are\\nrelated to a century-old work of Kasner, in which he conjectured that certain\\nsequences arising from complex analysis may have a quantum interpretation.\\nThese numbers also appear in the case of Kerr black holes, but the explanation\\nis not as straightforward. The Kasner ratio may also be relevant for\\nunderstanding the random matrix and random graph approaches to black hole\\nphysics, such as fast scrambling of quantum information, via a bound related to\\nRamanujan graph. Intriguingly, some other pure mathematical problems in complex\\nanalysis, notably complex interpolation in the unit disk, appear to share some\\nmathematical expressions with the black hole problem and thus also involve the\\nKasner ratio.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08236\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08236","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在黑洞物理学的不同背景下,都会出现$\sqrt{8/9}=2\sqrt{2}/3\approx0.9428$和$\sqrt{3}/2\approx0.866$这两个比值,它们分别是赖斯纳-诺德斯特朗(Reissner-Nordstr\"om)黑洞和克尔(Kerr)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,就赖斯纳-诺德斯特朗黑洞而言,我把这些比率与地平线面积的量子化或熵的量子化联系起来。此外,这些比值还与卡斯纳的一项百年前的工作有关,在这项工作中,他猜想由复数分析产生的某些序列可能具有量子解释。卡斯纳比率也可能与理解黑洞物理学中的随机矩阵和随机图方法有关,例如通过与拉玛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某些数学表达式,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。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Black Holes, Complex Curves, and Graph Theory: Revising a Conjecture by Kasner
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Holomorphic approximation by polynomials with exponents restricted to a convex cone The Denjoy-Wolff Theorem in simply connected domains Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean $L^2$-vanishing theorem and a conjecture of Kollár Nevanlinna Theory on Complete Kähler Connected Sums With Non-parabolic Ends
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1