(2+2) 哈密顿还原中的恩斯特方程的精确解

IF 0.8 4区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
Jong Hyuk Yoon, Yeongji Kim, Seung Hun Oh
{"title":"(2+2) 哈密顿还原中的恩斯特方程的精确解","authors":"Jong Hyuk Yoon,&nbsp;Yeongji Kim,&nbsp;Seung Hun Oh","doi":"10.1007/s40042-024-01060-4","DOIUrl":null,"url":null,"abstract":"<div><p>We apply the method of Hamiltonian reduction without isometry as a way to find exact solutions to Einstein’s equations. To find exact solutions, we introduce two spatial Killing vector fields to the Einstein’s equations obtained through the Hamiltonian reduction, and derive the Ernst-like equation in the privileged coordinates. By solving the Ernst-like equation, we found a four-parameter family of exact solutions, one of which is interpreted as a deformation of the general Kasner spacetime. We extend our method to spacetimes where two independent gravitational degrees of freedom co-exist and interact with each other, and obtain a set of two partial differential equations satisfied by them. If we substitute a pre-fixed diagonal mode into these equations, and then the equations reduce to a single non-linear partial differential equation, which is interpreted as the equation of non-diagonal mode of gravitational waves propagating on the “background” spacetime determined by the diagonal mode. We choose three simplest “background” spacetimes, and discuss the corresponding non-diagonal modes in each case.</p></div>","PeriodicalId":677,"journal":{"name":"Journal of the Korean Physical Society","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact solutions to Ernst-like equation in (2+2) Hamiltonian reduction\",\"authors\":\"Jong Hyuk Yoon,&nbsp;Yeongji Kim,&nbsp;Seung Hun Oh\",\"doi\":\"10.1007/s40042-024-01060-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We apply the method of Hamiltonian reduction without isometry as a way to find exact solutions to Einstein’s equations. To find exact solutions, we introduce two spatial Killing vector fields to the Einstein’s equations obtained through the Hamiltonian reduction, and derive the Ernst-like equation in the privileged coordinates. By solving the Ernst-like equation, we found a four-parameter family of exact solutions, one of which is interpreted as a deformation of the general Kasner spacetime. We extend our method to spacetimes where two independent gravitational degrees of freedom co-exist and interact with each other, and obtain a set of two partial differential equations satisfied by them. If we substitute a pre-fixed diagonal mode into these equations, and then the equations reduce to a single non-linear partial differential equation, which is interpreted as the equation of non-diagonal mode of gravitational waves propagating on the “background” spacetime determined by the diagonal mode. We choose three simplest “background” spacetimes, and discuss the corresponding non-diagonal modes in each case.</p></div>\",\"PeriodicalId\":677,\"journal\":{\"name\":\"Journal of the Korean Physical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Physical Society\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40042-024-01060-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Physical Society","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s40042-024-01060-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

我们采用不等距的哈密顿还原法来寻找爱因斯坦方程的精确解。为了找到精确解,我们在通过汉密尔顿还原法得到的爱因斯坦方程中引入了两个空间基林向量场,并推导出特权坐标下的恩斯特方程。通过求解恩斯特方程,我们发现了一个四参数精确解系列,其中一个可以解释为一般卡斯纳时空的变形。我们将方法扩展到两个独立引力自由度共存并相互作用的时空,并得到了由它们满足的两个偏微分方程组。如果我们将一个预先固定的对角模式代入这些方程,那么这些方程就会简化为一个单一的非线性偏微分方程,它被解释为在由对角模式决定的 "背景 "时空中传播的引力波的非对角模式方程。我们选择三种最简单的 "背景 "时空,讨论每种情况下相应的非对角模式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exact solutions to Ernst-like equation in (2+2) Hamiltonian reduction

We apply the method of Hamiltonian reduction without isometry as a way to find exact solutions to Einstein’s equations. To find exact solutions, we introduce two spatial Killing vector fields to the Einstein’s equations obtained through the Hamiltonian reduction, and derive the Ernst-like equation in the privileged coordinates. By solving the Ernst-like equation, we found a four-parameter family of exact solutions, one of which is interpreted as a deformation of the general Kasner spacetime. We extend our method to spacetimes where two independent gravitational degrees of freedom co-exist and interact with each other, and obtain a set of two partial differential equations satisfied by them. If we substitute a pre-fixed diagonal mode into these equations, and then the equations reduce to a single non-linear partial differential equation, which is interpreted as the equation of non-diagonal mode of gravitational waves propagating on the “background” spacetime determined by the diagonal mode. We choose three simplest “background” spacetimes, and discuss the corresponding non-diagonal modes in each case.

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
Journal of the Korean Physical Society
Journal of the Korean Physical Society PHYSICS, MULTIDISCIPLINARY-
CiteScore
1.20
自引率
16.70%
发文量
276
审稿时长
5.5 months
期刊介绍: The Journal of the Korean Physical Society (JKPS) covers all fields of physics spanning from statistical physics and condensed matter physics to particle physics. The manuscript to be published in JKPS is required to hold the originality, significance, and recent completeness. The journal is composed of Full paper, Letters, and Brief sections. In addition, featured articles with outstanding results are selected by the Editorial board and introduced in the online version. For emphasis on aspect of international journal, several world-distinguished researchers join the Editorial board. High quality of papers may be express-published when it is recommended or requested.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信