{"title":"The Jacobi metric approach for dynamical wormholes","authors":"Álvaro Duenas-Vidal, Oscar Lasso Andino","doi":"10.1007/s10714-022-03060-w","DOIUrl":null,"url":null,"abstract":"<div><p>We present the Jacobi metric formalism for dynamical wormholes. We show that in isotropic dynamical spacetimes , a first integral of the geodesic equations can be found using the Jacobi metric, and without any use of geodesic equation. This enables us to reduce the geodesic motion in dynamical wormholes to a dynamics defined in a Riemannian manifold. Then, making use of the Jacobi formalism, we study the circular stable orbits in the Jacobi metric framework for the dynamical wormhole background. Finally, we also show that the Gaussian curvature of the family of Jacobi metrics is directly related, as in the static case, to the flare-out condition of the dynamical wormhole, giving a way to characterize a wormhole spacetime by the sign of the Gaussian curvature of its Jacobi metric only.\n</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"55 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-022-03060-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: 1
Abstract
We present the Jacobi metric formalism for dynamical wormholes. We show that in isotropic dynamical spacetimes , a first integral of the geodesic equations can be found using the Jacobi metric, and without any use of geodesic equation. This enables us to reduce the geodesic motion in dynamical wormholes to a dynamics defined in a Riemannian manifold. Then, making use of the Jacobi formalism, we study the circular stable orbits in the Jacobi metric framework for the dynamical wormhole background. Finally, we also show that the Gaussian curvature of the family of Jacobi metrics is directly related, as in the static case, to the flare-out condition of the dynamical wormhole, giving a way to characterize a wormhole spacetime by the sign of the Gaussian curvature of its Jacobi metric only.
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.
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