{"title":"Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems","authors":"","doi":"10.1134/s0040577924020041","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class. </p> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924020041","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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