{"title":"Axially Symmetric Rotating Black Holes, Boyer–Lindquist Coordinates, and Regularity Conditions on Horizons","authors":"H. V. Ovcharenko, O. B. Zaslavskii","doi":"10.1134/S0202289323030131","DOIUrl":null,"url":null,"abstract":"<p>We consider the metric of an axially symmetric rotating black hole. We do not specify the concrete form of a metric and rely on its behavior near the horizon only. Typically, it is characterized (in the coordinates that generalize the Boyer–Lindquist ones) by two integers <span>\\(p\\)</span> and <span>\\(q\\)</span> that enter asymptotic expansions of the time and radial metric coefficients in the main approximation. For given <span>\\(p\\)</span> and <span>\\(q\\)</span> we find a general form for which the metric is regular, and how the expansions of the metric coefficients look like. We compare two types of requirement: (i) boundedness of curvature invariants, (ii) boundedness of separate components of the curvature tensor in a freely falling frame. Analysis is done for nonextremal, extremal and ultraextremal horizons separately.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"29 3","pages":"269 - 282"},"PeriodicalIF":1.2000,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289323030131","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the metric of an axially symmetric rotating black hole. We do not specify the concrete form of a metric and rely on its behavior near the horizon only. Typically, it is characterized (in the coordinates that generalize the Boyer–Lindquist ones) by two integers \(p\) and \(q\) that enter asymptotic expansions of the time and radial metric coefficients in the main approximation. For given \(p\) and \(q\) we find a general form for which the metric is regular, and how the expansions of the metric coefficients look like. We compare two types of requirement: (i) boundedness of curvature invariants, (ii) boundedness of separate components of the curvature tensor in a freely falling frame. Analysis is done for nonextremal, extremal and ultraextremal horizons separately.
期刊介绍:
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community