The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914075089305600 |
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| author | Bubuianu, Laurenţiu Seti, Julia O. Singleton, Douglas Stavrinos, Panayiotis Vacaru, Sergiu I. Veliev, Elşen Veli |
| author_facet | Bubuianu, Laurenţiu Seti, Julia O. Singleton, Douglas Stavrinos, Panayiotis Vacaru, Sergiu I. Veliev, Elşen Veli |
| contents | This article is a status report on the Anholonomic Frame and Connection Deformation Method, AFCDM, for constructing generic off-diagonal exact and parametric solutions in general relativity, GR, relativistic geometric flows, and modified gravity theories, MGTs. Such models can be generalized to nonassociative and noncommutative star products on phase spaces and modelled equivalently as nonassociative Finsler-Lagrange-Hamilton geometries. Our approach involves a nonholonomic geometric reformulation of classical models of gravitational and matter fields described by Lagrange and Hamilton densities on relativistic phase spaces. Using nonholonomic dyadic variables, the Einstein equations in GR and MGTs can be formulated as systems of nonlinear partial differential equations(PDEs), which can be decoupled and integrated in some general off-diagonal forms. In this approach, the Lagrange and Hamilton dynamics and related models of classical and quantum evolution are equivalently described in terms of generalized Finsler-like or canonical metrics and (nonlinear) connection structures on deformed phase spaces defined by solutions of modified Einstein equations. New classes of exact and parametric solutions in (nonassociative) MGTs are formulated in terms of generating and integration functions and generating effective/ matter sources. The physical interpretation of respective classes of solutions depends on the type of (non) linear symmetries, prescribed boundary/ asymptotic conditions, or posed Cauchy problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories Bubuianu, Laurenţiu Seti, Julia O. Singleton, Douglas Stavrinos, Panayiotis Vacaru, Sergiu I. Veliev, Elşen Veli General Relativity and Quantum Cosmology High Energy Physics - Theory This article is a status report on the Anholonomic Frame and Connection Deformation Method, AFCDM, for constructing generic off-diagonal exact and parametric solutions in general relativity, GR, relativistic geometric flows, and modified gravity theories, MGTs. Such models can be generalized to nonassociative and noncommutative star products on phase spaces and modelled equivalently as nonassociative Finsler-Lagrange-Hamilton geometries. Our approach involves a nonholonomic geometric reformulation of classical models of gravitational and matter fields described by Lagrange and Hamilton densities on relativistic phase spaces. Using nonholonomic dyadic variables, the Einstein equations in GR and MGTs can be formulated as systems of nonlinear partial differential equations(PDEs), which can be decoupled and integrated in some general off-diagonal forms. In this approach, the Lagrange and Hamilton dynamics and related models of classical and quantum evolution are equivalently described in terms of generalized Finsler-like or canonical metrics and (nonlinear) connection structures on deformed phase spaces defined by solutions of modified Einstein equations. New classes of exact and parametric solutions in (nonassociative) MGTs are formulated in terms of generating and integration functions and generating effective/ matter sources. The physical interpretation of respective classes of solutions depends on the type of (non) linear symmetries, prescribed boundary/ asymptotic conditions, or posed Cauchy problems. |
| title | The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.02321 |