{"title":"无对数奇点的双曲面初始数据","authors":"Károly Csukás, István Rácz","doi":"10.1007/s10714-025-03424-y","DOIUrl":null,"url":null,"abstract":"<div><p>Andersson and Chruściel showed that generic asymptotically hyperboloidal initial data sets admit polyhomogeneous expansions, and that only a non-generic subclass of solutions of the conformal constraint equations is free of logarithmic singularities. The purpose of this work is twofold. First, within the evolutionary framework of the constraint equations, we show that the existence of a well-defined Bondi mass brings the asymptotically hyperboloidal initial data sets into a subclass whose Cauchy development guaranteed to admit a smooth boundary, by virtue of the results of Andersson and Chruściel. Second, by generalizing a recent result of Beyer and Ritchie, we show that the existence of well-defined Bondi mass and angular momentum, together with some mild restrictions on the free data, implies that the generic solutions of the parabolic-hyperbolic form of the constraint equations are completely free of logarithmic singularities. We also provide numerical evidence to show that in the vicinity of Kerr, asymptotically hyperboloidal initial data without logarithmic singularities can indeed be constructed.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 6","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-025-03424-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Hyperboloidal initial data without logarithmic singularities\",\"authors\":\"Károly Csukás, István Rácz\",\"doi\":\"10.1007/s10714-025-03424-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Andersson and Chruściel showed that generic asymptotically hyperboloidal initial data sets admit polyhomogeneous expansions, and that only a non-generic subclass of solutions of the conformal constraint equations is free of logarithmic singularities. The purpose of this work is twofold. First, within the evolutionary framework of the constraint equations, we show that the existence of a well-defined Bondi mass brings the asymptotically hyperboloidal initial data sets into a subclass whose Cauchy development guaranteed to admit a smooth boundary, by virtue of the results of Andersson and Chruściel. Second, by generalizing a recent result of Beyer and Ritchie, we show that the existence of well-defined Bondi mass and angular momentum, together with some mild restrictions on the free data, implies that the generic solutions of the parabolic-hyperbolic form of the constraint equations are completely free of logarithmic singularities. We also provide numerical evidence to show that in the vicinity of Kerr, asymptotically hyperboloidal initial data without logarithmic singularities can indeed be constructed.</p></div>\",\"PeriodicalId\":578,\"journal\":{\"name\":\"General Relativity and Gravitation\",\"volume\":\"57 6\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10714-025-03424-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Relativity and Gravitation\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10714-025-03424-y\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-025-03424-y","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Hyperboloidal initial data without logarithmic singularities
Andersson and Chruściel showed that generic asymptotically hyperboloidal initial data sets admit polyhomogeneous expansions, and that only a non-generic subclass of solutions of the conformal constraint equations is free of logarithmic singularities. The purpose of this work is twofold. First, within the evolutionary framework of the constraint equations, we show that the existence of a well-defined Bondi mass brings the asymptotically hyperboloidal initial data sets into a subclass whose Cauchy development guaranteed to admit a smooth boundary, by virtue of the results of Andersson and Chruściel. Second, by generalizing a recent result of Beyer and Ritchie, we show that the existence of well-defined Bondi mass and angular momentum, together with some mild restrictions on the free data, implies that the generic solutions of the parabolic-hyperbolic form of the constraint equations are completely free of logarithmic singularities. We also provide numerical evidence to show that in the vicinity of Kerr, asymptotically hyperboloidal initial data without logarithmic singularities can indeed be constructed.
期刊介绍:
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.