{"title":"Self-gravitating anisotropic fluid. III: relativistic theory","authors":"Tom Cadogan, Eric Poisson","doi":"10.1007/s10714-024-03305-w","DOIUrl":null,"url":null,"abstract":"<div><p>This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In the first paper we placed our work in context and provided an overview of the results obtained in the second and third papers. In the second paper we took the necessary step of elaborating a Newtonian theory, and exploited it to build anisotropic stellar models. In this third paper we elevate the theory to general relativity, and apply it to the construction of relativistic stellar models. The relativistic theory is crafted by promoting the fluid variables to a curved spacetime, and promoting the gravitational potential to the spacetime metric. Thus, the director vector, which measures the local magnitude and direction of the anisotropy, is now a four-dimensional vector, and to keep the number of independent degrees of freedom at three, it is required to be orthogonal to the fluid’s velocity vector. The Newtonian action is then generalized in a direct and natural way, and dynamical equations for all the relevant variables are once more obtained through a variational principle. We specialize our relativistic theory of a self-gravitating anisotropic fluid to static and spherically symmetric configurations, and thus obtain models of anisotropic stars in general relativity. As in the Newtonian setting, the models feature a transition from an anisotropic phase at high density to an isotropic phase at low density. Our survey of stellar models reveals that for the same equations of state and the same central density, anisotropic stars are always less compact than isotropic stars.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"56 10","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-024-03305-w","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}
引用次数: 0
Abstract
This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In the first paper we placed our work in context and provided an overview of the results obtained in the second and third papers. In the second paper we took the necessary step of elaborating a Newtonian theory, and exploited it to build anisotropic stellar models. In this third paper we elevate the theory to general relativity, and apply it to the construction of relativistic stellar models. The relativistic theory is crafted by promoting the fluid variables to a curved spacetime, and promoting the gravitational potential to the spacetime metric. Thus, the director vector, which measures the local magnitude and direction of the anisotropy, is now a four-dimensional vector, and to keep the number of independent degrees of freedom at three, it is required to be orthogonal to the fluid’s velocity vector. The Newtonian action is then generalized in a direct and natural way, and dynamical equations for all the relevant variables are once more obtained through a variational principle. We specialize our relativistic theory of a self-gravitating anisotropic fluid to static and spherically symmetric configurations, and thus obtain models of anisotropic stars in general relativity. As in the Newtonian setting, the models feature a transition from an anisotropic phase at high density to an isotropic phase at low density. Our survey of stellar models reveals that for the same equations of state and the same central density, anisotropic stars are always less compact than isotropic stars.
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.