Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds
We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/4/247 |
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| author | Mahouton Norbert Hounkonnou Mahougnon Justin Landalidji Melanija Mitrović |
| author_facet | Mahouton Norbert Hounkonnou Mahougnon Justin Landalidji Melanija Mitrović |
| author_sort | Mahouton Norbert Hounkonnou |
| collection | DOAJ |
| description | We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian–Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson–Schwarzschild and Friedmann–Lemaître–Robertson–Walker (FLRW) manifolds, and derive the related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion. |
| first_indexed | 2024-03-09T04:09:47Z |
| format | Article |
| id | doaj.art-89435787cef94d00b2280281cdea7e72 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T04:09:47Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-89435787cef94d00b2280281cdea7e722023-12-03T14:02:30ZengMDPI AGUniverse2218-19972022-04-018424710.3390/universe8040247Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson ManifoldsMahouton Norbert Hounkonnou0Mahougnon Justin Landalidji1Melanija Mitrović2International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Cotonou 072 BP 50, BeninInternational Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Cotonou 072 BP 50, BeninInternational Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Cotonou 072 BP 50, BeninWe show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian–Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson–Schwarzschild and Friedmann–Lemaître–Robertson–Walker (FLRW) manifolds, and derive the related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.https://www.mdpi.com/2218-1997/8/4/247Einstein field equationrecursion operatorNoether symmetrymaster symmetryconformable differentialPoisson manifold |
| spellingShingle | Mahouton Norbert Hounkonnou Mahougnon Justin Landalidji Melanija Mitrović Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds Universe Einstein field equation recursion operator Noether symmetry master symmetry conformable differential Poisson manifold |
| title | Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds |
| title_full | Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds |
| title_fullStr | Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds |
| title_full_unstemmed | Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds |
| title_short | Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds |
| title_sort | einstein field equation recursion operators noether and master symmetries in conformable poisson manifolds |
| topic | Einstein field equation recursion operator Noether symmetry master symmetry conformable differential Poisson manifold |
| url | https://www.mdpi.com/2218-1997/8/4/247 |
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