均匀球的相对论角动量与旋转半径和角速度的关系

Sergey G. Fedosin
{"title":"均匀球的相对论角动量与旋转半径和角速度的关系","authors":"Sergey G. Fedosin","doi":"10.18052/www.scipress.com/ifsl.15.9","DOIUrl":null,"url":null,"abstract":"In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.","PeriodicalId":262344,"journal":{"name":"International Frontier Science Letters","volume":"120-121 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation\",\"authors\":\"Sergey G. Fedosin\",\"doi\":\"10.18052/www.scipress.com/ifsl.15.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.\",\"PeriodicalId\":262344,\"journal\":{\"name\":\"International Frontier Science Letters\",\"volume\":\"120-121 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Frontier Science Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18052/www.scipress.com/ifsl.15.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Frontier Science Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18052/www.scipress.com/ifsl.15.9","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

在狭义相对论的框架下,利用初等公式导出了理想均匀球旋转的相对论角动量的计算公式。这种球的转动惯量是角速度的非线性函数。对中子星PSR J1614-2230的应用表明,由于相对论修正,恒星的角动量比非相对论公式增加了十倍。对质子和中子星PSR j1748 -2446的表面运动速度进行了计算,分别达到光速的30%和19%数量级。利用均匀球的相对论角动量公式,可以很容易地得到薄球壳的角动量公式,这取决于它的厚度、半径、质量密度和旋转角速度。因此,考虑一个由一组这样的壳体组成的球体,就有可能精确地确定它的角动量为所有壳体角动量的总和。基于球的表面以光速旋转和基于重力束缚体在引力和向心力平衡下的完整性条件,给出了球的最大可能角动量的两种表达式。与广义相对论的结果比较表明,极端克尔黑洞的角动量差约为25%。
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
On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation
In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.
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
On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation Fixed Points and Stability Analysis in the Motion of Human Heart Valve Leaflet On Solution of Singular Integral Equations by Operator Method The Generalized Poynting Theorem for the General Field and Solution of the 4/3 Problem Group Function of Income Distribution in Society
×
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