Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva
{"title":"虫洞的暗能量和暗物质构型以及非度量利玛窦流和 $F(R,T,Q,T_{m})$ 引力的溶解性层次结构","authors":"Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva","doi":"arxiv-2402.19362","DOIUrl":null,"url":null,"abstract":"We extend the anholonomic frame and connection deformation method, AFCDM, for\nconstructing exact and parametric solutions in general relativity, GR, to\ngeometric flow models and modified gravity theories, MGTs, with nontrivial\ntorsion and nonmetricity fields. Following abstract geometric or variational\nmethods, we can derive corresponding systems of nonmetric gravitational and\nmatter field equations which consist of very sophisticated systems of coupled\nnonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and\napplying the AFCDM, we prove that such systems of PDEs can be decoupled and\nintegrated in general forms for generic off-diagonal metric structures and\ngeneralized affine connections. We generate new classes of quasi-stationary\nsolutions (which do not depend on time like coordinates) and study the physical\nproperties of some physically important examples. Such exact or parametric\nsolutions are determined by nonmetric solitonic distributions and/or\nellipsoidal deformations of wormhole hole configurations. It is not possible to\ndescribe the thermodynamic properties of such solutions in the framework of the\nBekenstein-Hawking paradigm because such metrics do not involve, in general,\ncertain horizons, duality, or holographic configurations. Nevertheless, we can\nalways elaborate on associated Grigori Perelman thermodynamic models elaborated\nfor nonmetric geometric flows. In explicit form, applying the AFCDM, we\nconstruct and study the physical implications of new classes of traversable\nwormhole solutions describing solitonic deformation and dissipation of\nnon-Riemannian geometric objects. Such models with nontrivial gravitational\noff-diagonal vacuum are important for elaborating models of dark energy and\ndark matter involving wormhole configurations and solitonic-type structure\nformation.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_{m})$ gravity\",\"authors\":\"Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva\",\"doi\":\"arxiv-2402.19362\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the anholonomic frame and connection deformation method, AFCDM, for\\nconstructing exact and parametric solutions in general relativity, GR, to\\ngeometric flow models and modified gravity theories, MGTs, with nontrivial\\ntorsion and nonmetricity fields. Following abstract geometric or variational\\nmethods, we can derive corresponding systems of nonmetric gravitational and\\nmatter field equations which consist of very sophisticated systems of coupled\\nnonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and\\napplying the AFCDM, we prove that such systems of PDEs can be decoupled and\\nintegrated in general forms for generic off-diagonal metric structures and\\ngeneralized affine connections. We generate new classes of quasi-stationary\\nsolutions (which do not depend on time like coordinates) and study the physical\\nproperties of some physically important examples. Such exact or parametric\\nsolutions are determined by nonmetric solitonic distributions and/or\\nellipsoidal deformations of wormhole hole configurations. It is not possible to\\ndescribe the thermodynamic properties of such solutions in the framework of the\\nBekenstein-Hawking paradigm because such metrics do not involve, in general,\\ncertain horizons, duality, or holographic configurations. Nevertheless, we can\\nalways elaborate on associated Grigori Perelman thermodynamic models elaborated\\nfor nonmetric geometric flows. In explicit form, applying the AFCDM, we\\nconstruct and study the physical implications of new classes of traversable\\nwormhole solutions describing solitonic deformation and dissipation of\\nnon-Riemannian geometric objects. Such models with nontrivial gravitational\\noff-diagonal vacuum are important for elaborating models of dark energy and\\ndark matter involving wormhole configurations and solitonic-type structure\\nformation.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2402.19362\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.19362","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_{m})$ gravity
We extend the anholonomic frame and connection deformation method, AFCDM, for
constructing exact and parametric solutions in general relativity, GR, to
geometric flow models and modified gravity theories, MGTs, with nontrivial
torsion and nonmetricity fields. Following abstract geometric or variational
methods, we can derive corresponding systems of nonmetric gravitational and
matter field equations which consist of very sophisticated systems of coupled
nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and
applying the AFCDM, we prove that such systems of PDEs can be decoupled and
integrated in general forms for generic off-diagonal metric structures and
generalized affine connections. We generate new classes of quasi-stationary
solutions (which do not depend on time like coordinates) and study the physical
properties of some physically important examples. Such exact or parametric
solutions are determined by nonmetric solitonic distributions and/or
ellipsoidal deformations of wormhole hole configurations. It is not possible to
describe the thermodynamic properties of such solutions in the framework of the
Bekenstein-Hawking paradigm because such metrics do not involve, in general,
certain horizons, duality, or holographic configurations. Nevertheless, we can
always elaborate on associated Grigori Perelman thermodynamic models elaborated
for nonmetric geometric flows. In explicit form, applying the AFCDM, we
construct and study the physical implications of new classes of traversable
wormhole solutions describing solitonic deformation and dissipation of
non-Riemannian geometric objects. Such models with nontrivial gravitational
off-diagonal vacuum are important for elaborating models of dark energy and
dark matter involving wormhole configurations and solitonic-type structure
formation.